Yahya Ould Hamidoune’s mathematical journey: a critical review of his work. (English) Zbl 1292.05002
Summary: We present the mathematical work of Yahya Ould Hamidoune, emphasizing his main achievements, notably in graph theory and additive combinatorics.
MSC:
| 05-03 | History of combinatorics |
| 11-03 | History of number theory |
| 01A70 | Biographies, obituaries, personalia, bibliographies |
| 05Cxx | Graph theory |
| 11B30 | Arithmetic combinatorics; higher degree uniformity |
Biographic References:
Hamidoune, Yahya OuldReferences:
| [1] | Hamidoune, Y. O., Sur les atomes d’un graphe orienté, C.R. Acad. Sci., Paris A-B, 284, 1253-1256 (1977) · Zbl 0352.05035 |
| [2] | Hamidoune, Y. O., Sur les sommets de demi-degré \(h\) d’un graphe fortement \(h\)-connexe minimal, C.R. Acad. Sci., Paris A-B, 286, 863-865 (1978) · Zbl 0376.05039 |
| [4] | Hamidoune, Y. O., Sur les parcours hamiltoniens dans les graphes orientés, Discrete Math., 26, 227-234 (1979) · Zbl 0417.05044 |
| [5] | Hamidoune, Y. O., On the decomposition of a minimally strongly \(h\)-connected digraph into \(h + 1\) acircuitic subgraphs, Discrete Math., 31, 89-90 (1980) · Zbl 0437.05027 |
| [6] | Hamidoune, Y. O., A property of \(a\)-fragments of a digraph, Discrete Math., 31, 105-106 (1980) · Zbl 0438.05039 |
| [7] | Hamidoune, Y. O., On critically \(h\)-connected simple graphs, Discrete Math., 32, 257-262 (1980) · Zbl 0452.05043 |
| [8] | Hamidoune, Y. O., Connectivity of transitive digraphs and a combinatorial property of finite groups, Proc. Colloq., Univ. Montréal, Montreal, Quebec, 1979, Part I, Ann. Discrete Math. Vol. 8. Proc. Colloq., Univ. Montréal, Montreal, Quebec, 1979, Part I, Ann. Discrete Math. Vol. 8, Combinatorics, 79, 61-64 (1980) · Zbl 0474.05035 |
| [10] | Hamidoune, Y. O., Quelques problèmes de connexité dans les graphes orientés, J. Combin. Theory Ser. B, 30, 1-10 (1981) · Zbl 0475.05039 |
| [11] | Hamidoune, Y. O., On multiply critically \(h\)-connected graphs, J. Combin. Theory Ser. B, 30, 108-112 (1981) · Zbl 0472.05040 |
| [12] | Hamidoune, Y. O., An application of connectivity theory in graphs to factorizations of elements in groups, European J. Combin., 2, 349-355 (1981) · Zbl 0473.05032 |
| [13] | Hamidoune, Y. O., A note on the girth of digraphs, Combinatorica, 2, 143-147 (1982) · Zbl 0515.05033 |
| [14] | Hamidoune, Y. O., On a conjecture of Entringer and Slater, Discrete Math., 41, 323-326 (1982) · Zbl 0496.05034 |
| [15] | Duchet, P.; Hamidoune, Y. O.; Las Vergnas, M.; Meyniel, H., Representing a planar graph by vertical lines joining different levels, Discrete Math., 46, 319-321 (1983) · Zbl 0516.05023 |
| [16] | Hamidoune, Y. O.; Las Vergnas, M., Jeux de commutation orientés sur les graphes et les matroïdes, C.R. Acad. Sci., Paris I, 298, 497-499 (1984) · Zbl 0559.90099 |
| [17] | Hamidoune, Y. O., On the connectivity of Cayley digraphs, European J. Combin., 5, 309-312 (1984) · Zbl 0561.05028 |
| [18] | Hamidoune, Y. O., Sur la séparation dans les graphes de Cayley abéliens, Discrete Math., 55, 323-326 (1985) · Zbl 0567.05027 |
| [19] | Hamidoune, Y. O.; Las Vergnas, M., The directed Shannon switching game and the one-way game, (Graph Theory with Applications to Algorithms and Computer Science (Kalamazoo, Mich., 1984) (1985), Wiley-Intersci. Publ., Wiley: Wiley-Intersci. Publ., Wiley New York), 391-400 · Zbl 0587.90101 |
| [20] | Hamidoune, Y. O.; Las Vergnas, M., Directed switching games on graphs and matroids, J. Combin. Theory Ser. B, 40, 237-269 (1986) · Zbl 0589.90109 |
| [21] | Hamidoune, Y. O.; Las Vergnas, M., A solution to the box game, Discrete Math., 65, 157-171 (1987) · Zbl 0631.90091 |
| [22] | Hamidoune, Y. O., A note on minimal directed graphs with given girth, J. Combin. Theory Ser. B, 43, 343-348 (1987) · Zbl 0643.05036 |
| [23] | Hamidoune, Y. O., On a pursuit game of Cayley digraphs, European J. Combin., 8, 289-295 (1987) · Zbl 0639.05026 |
| [24] | Duchet, P.; Hamidoune, Y. O.; Meyniel, H., Sur les quasi-noyaux d’un graphe, Discrete Math., 65, 231-235 (1987) · Zbl 0623.05020 |
| [25] | Hamidoune, Y. O.; Las Vergnas, M., Local edge-connectivity in regular bipartite graphs, J. Combin. Theory Ser. B, 44, 370-371 (1988) · Zbl 0662.05042 |
| [26] | Hamidoune, Y. O.; Las Vergnas, M., A solution to the misère Shannon switching game, Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986). Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986), Discrete Math., 72, 163-166 (1988) · Zbl 0656.90099 |
| [27] | Hamidoune, Y. O.; Roeder, D.; Janke, S.; Feil, T.; Koo, R., The probability of splitters in a list, J. Algorithms, 10, 151-154 (1989) · Zbl 0685.68057 |
| [28] | Hamidoune, Y. O.; Salaün, I., On the independence numbers of a matroid, J. Combin. Theory Ser. B, 47, 146-152 (1989) · Zbl 0629.05020 |
| [29] | Hamidoune, Y. O., Sur les atomes d’un graphe de Cayley infini, Discrete Math., 73, 297-300 (1989) · Zbl 0663.05057 |
| [30] | Hamidoune, Y. O., Factorisations courtes dans un groupe fini, First Montreal Conference on Combinatorics and Computer Science, 1987. First Montreal Conference on Combinatorics and Computer Science, 1987, Discrete Appl. Math., 24, 153-165 (1989) · Zbl 0681.20019 |
| [31] | Hamidoune, Y. O., On the numbers of independent \(k\)-sets in a claw free graph, J. Combin. Theory Ser. B, 50, 241-244 (1990) · Zbl 0743.05029 |
| [32] | Hamidoune, Y. O., Connectivité des graphes de Cayley abéliens sans \(K_4\), Discrete Math., 83, 21-26 (1990) · Zbl 0789.05052 |
| [33] | Hamidoune, Y. O., A note on the addition of residues, Graphs Combin., 6, 147-152 (1990) · Zbl 0745.11009 |
| [34] | Dias da Silva, J.; Hamidoune, Y. O., A note on the minimal polynomial of the Kronecker sum of two linear operators, Linear Algebra Appl., 141, 283-287 (1990) · Zbl 0709.15002 |
| [35] | Hamidoune, Y. O., On some graphic aspects of addition theorems, (Topics in Combinatorics and Graph Theory (Oberwolfach, 1990) (1990), Physica: Physica Heidelberg), 311-318 · Zbl 0721.05030 |
| [36] | Hamidoune, Y. O.; Tindell, R., Vertex transitivity and super line connectedness, SIAM J. Discrete Math., 3, 524-530 (1990) · Zbl 0789.05053 |
| [37] | Hamidoune, Y. O.; Lladó, A.; Serra, O., Vosperian and superconnected abelian Cayley digraphs, Graphs Combin., 7, 143-152 (1991) · Zbl 0736.05047 |
| [38] | Hamidoune, Y. O., On the subsets product in finite groups, European J. Combin., 12, 211-221 (1991) · Zbl 0736.20013 |
| [39] | Hamidoune, Y. O., Combinatorial additive number theory and Cayley graphs, (Graph Theory, Combinatorics, and Applications. Vol. 2 (Kalamazoo, MI, 1988) (1991), Wiley-Intersci. Publ., Wiley: Wiley-Intersci. Publ., Wiley New York), 615-620 · Zbl 0841.05041 |
| [40] | Hamidoune, Y. O., On a subgroup contained in some words with a bounded length, Discrete Math., 103, 171-176 (1992) · Zbl 0773.20004 |
| [41] | Hamidoune, Y. O.; Lladó, A.; Serra, O., The connectivity of hierarchical Cayley digraphs, Discrete Appl. Math., 37/38, 275-280 (1992) · Zbl 0776.05048 |
| [42] | Hamidoune, Y. O., A generalization of an addition theorem of Shatrowsky, European J. Combin., 13, 249-255 (1992) · Zbl 0768.05051 |
| [43] | Hamidoune, Y. O., The minimum order of a Cayley graph with given degree and diameter, Networks, 23, 283-287 (1993) · Zbl 0778.05039 |
| [44] | Delorme, C.; Hamidoune, Y. O., On products of sets in groups, Graphs Combin., 10, 101-104 (1994) · Zbl 0803.05024 |
| [45] | Dias da Silva, J. A.; Hamidoune, Y. O., Cyclic spaces for Grassmann derivatives and additive theory, Bull. London Math. Soc., 26, 140-146 (1994) · Zbl 0819.11007 |
| [46] | Hamidoune, Y. O., The representation of some integers as a subset sum, Bull. London Math. Soc., 26, 557-563 (1994) · Zbl 0838.11019 |
| [48] | Hamidoune, Y. O.; Lladó, A.; Serra, O., Minimum order of loop networks of given degree and girth, Graphs Combin., 11, 131-138 (1995) · Zbl 0824.05029 |
| [49] | Hamidoune, Y. O., On weighted sequence sums, Combin. Probab. Comput., 4, 363-367 (1995) · Zbl 0848.20049 |
| [51] | Hamidoune, Y. O., An isoperimetric method in additive theory, J. Algebra, 179, 622-630 (1996) · Zbl 0842.20029 |
| [52] | Hamidoune, Y. O., Additive group theory applied to network topology, (Combinatorial Network Theory. Combinatorial Network Theory, Appl. Optim., vol. 1 (1996), Kluwer Acad. Publ.: Kluwer Acad. Publ. Dordrecht), 1-39 · Zbl 0845.05051 |
| [53] | Hamidoune, Y. O.; Serra, O., On small cuts separating an abelian Cayley graph into two equal parts, Math. Syst. Theory, 29, 407-409 (1996) · Zbl 0856.05050 |
| [54] | Hamidoune, Y. O.; Lladó, A.; Serra, O., Small cutsets in quasiminimal Cayley graphs, Discrete Math., 159, 131-142 (1996) · Zbl 0862.05051 |
| [55] | Hamidoune, Y. O.; Rødseth, Ø., On bases for \(\sigma \)-finite groups, Math. Scand., 78, 246-254 (1996) · Zbl 0877.11007 |
| [56] | Hamidoune, Y. O.; Zémor, G., On zero-free subset sums, Acta Arith., 78, 143-152 (1996) · Zbl 0863.11016 |
| [57] | Hamidoune, Y. O., On weighted sums in abelian groups, Discrete Math., 162, 127-132 (1996) · Zbl 0872.11016 |
| [58] | Hamidoune, Y. O., Subsets with small sums in abelian groups, I: the Vosper property, European J. Combin., 18, 541-556 (1997) · Zbl 0883.05065 |
| [59] | Hamidoune, Y. O.; Las Vergnas, M., Directed switching games, II. the arborescence game, Graphs and Combinatorics (Marseille, 1995). Graphs and Combinatorics (Marseille, 1995), Discrete Math., 165/166, 395-402 (1997) · Zbl 0873.90138 |
| [60] | Hamidoune, Y. O., Erdős-Heilbronn problem, (Encyclopaedia of Mathematics Supplement I (1997), Kluwer Acad. Publishers), 242 |
| [61] | Hamidoune, Y. O., Adding distinct congruence classes, Combin. Probab. Comput., 7, 81-87 (1998) · Zbl 0894.11004 |
| [62] | Hamidoune, Y. O., On the Diophantine Frobenius problem, Port. Math., 55, 425-449 (1998) · Zbl 0923.11044 |
| [63] | Gao, W.; Hamidoune, Y. O., Zero sums in abelian groups, Combin. Probab. Comput., 7, 261-263 (1998) · Zbl 1076.11501 |
| [64] | Hamidoune, Y. O.; Ordaz, O.; Ortuño, A., On a combinatorial theorem of Erdös, Ginzburg and Ziv, Combin. Probab. Comput., 7, 403-412 (1998) · Zbl 1057.05507 |
| [65] | Hamidoune, Y. O.; Lladó, A.; Serra, O., On subsets with small product in torsion-free groups, Combinatorica, 18, 529-540 (1998) · Zbl 0930.20034 |
| [66] | Gao, W.; Hamidoune, Y. O., On additive bases, Acta Arith., 88, 233-237 (1999) · Zbl 0935.11004 |
| [67] | Hamidoune, Y. O., On small subset product in a group, structure theory of set addition, Astérique, 258, 281-308 (1999) · Zbl 0945.20011 |
| [68] | Hamidoune, Y. O.; Lladó, A.; Serra, O., An isoperimetric problem in Cayley graphs, Theory Comput. Syst., 32, 507-516 (1999) · Zbl 0936.05054 |
| [69] | Hamidoune, Y. O.; Lladó, A.; Serra, O., On sets with a small subset sum, Combin. Probab. Comput., 8, 461-466 (1999) · Zbl 1109.11323 |
| [70] | Hamidoune, Y. O.; Lladó, A.; Serra, O., Sets with a small subset sum and a conjecture by Diderrich, (Paul Erdős and His Mathematics (Budapest, 1999) (1999), János Bolyai Math. Soc.: János Bolyai Math. Soc. Budapest), 99-101 · Zbl 1109.11324 |
| [71] | Hamidoune, Y. O.; Lladó, A.; Serra, O.; Tindell, R., On isoperimetric connectivity in vertex-transitive graphs, SIAM J. Discrete Math., 13, 139-144 (2000) · Zbl 0951.05051 |
| [72] | Hamidoune, Y. O., Subsets with a small sum II: the critical pair problem, European J. Combin., 21, 231-239 (2000) · Zbl 0941.05064 |
| [73] | Hamidoune, Y. O.; Rødseth, Ø., An inverse theorem modulo \(p\), Acta Arith., 92, 251-262 (2000) · Zbl 0945.11003 |
| [74] | Hamidoune, Y. O.; Lladó, A.; Serra, O., On restricted sums, Combin. Probab. Comput., 9, 513-518 (2000) · Zbl 0974.20043 |
| [75] | Hamidoune, Y. O., Some results in additive number theory I: the critical pair theory, Acta Arith., 96, 97-119 (2000) · Zbl 0985.11011 |
| [76] | Geroldinger, A.; Hamidoune, Y. O., Zero-sum-free sequences in cyclic groups and some arithmetical application, J. Théor. Nombres Bordeaux, 14, 221-239 (2002) · Zbl 1018.11011 |
| [77] | Hamidoune, Y. O.; Plagne, A., A generalization of Freiman’s \(3 k - 3\) theorem, Acta Arith., 103, 147-156 (2002) · Zbl 1007.11011 |
| [78] | Gao, W.; Hamidoune, Y. O.; Lladó, A.; Serra, O., Covering a finite abelian group by subset sums, Combinatorica, 23, 599-611 (2003) · Zbl 1049.11022 |
| [79] | Hamidoune, Y. O., Subsequence sums, Combin. Probab. Comput., 12, 413-425 (2003) · Zbl 1049.11024 |
| [80] | Hamidoune, Y. O.; Plagne, A., A new critical pair theorem applied to sum-free sets in abelian groups, Comment. Math. Helv., 79, 183-207 (2004) · Zbl 1045.11072 |
| [81] | Hamidoune, Y. O.; Quiroz, D., On subsequence weighted products, Combin. Probab. Comput., 14, 485-489 (2005) · Zbl 1095.20013 |
| [82] | Hamidoune, Y. O.; Plagne, A., A multiple set version of the \(3 k - 3\) theorem, Rev. Mat. Iberoam., 21, 133-161 (2005) · Zbl 1078.11059 |
| [83] | Hamidoune, Y. O.; Serra, O.; Zémor, G., On the critical pair theory in \(Z / p Z\), Acta Arith., 121, 99-115 (2006) · Zbl 1147.11060 |
| [84] | Hamidoune, Y. O., On iterated image size for point-symmetric relations, Combin. Probab. Comput., 17, 61-66 (2008) · Zbl 1154.05037 |
| [85] | Hamidoune, Y. O.; Serra, O.; Zémor, G., On the critical pair theory in abelian groups: beyond Chowla’s theorem, Combinatorica, 28, 441-467 (2008) · Zbl 1192.11071 |
| [86] | Hamidoune, Y. O.; Lladó, A.; Serra, O., On complete subsets of the cyclic group, J. Combin. Theory Ser. A, 115, 1279-1285 (2008) · Zbl 1192.11007 |
| [87] | Hamidoune, Y. O.; Serra, O.; Zémor, G., On some subgroup chains related to Kneser’s theorem, J. Théor. Nombres Bordeaux, 20, 125-130 (2008) · Zbl 1197.11016 |
| [88] | Hamidoune, Y. O., Some additive applications of the isoperimetric approach, Ann. Inst. Fourier (Grenoble), 58, 2007-2036 (2008) · Zbl 1173.05019 |
| [90] | Hamidoune, Y. O., A weighted generalization of Gao’s \(n + D - 1\) theorem, Combin. Probab. Comput., 17, 793-798 (2008) · Zbl 1198.11029 |
| [92] | Cilleruelo, J.; Hamidoune, Y. O.; Serra, O., On sums of dilates, Combin. Probab. Comput., 18, 871-880 (2009) · Zbl 1200.11007 |
| [93] | Hamidoune, Y. O., The isoperimetric method, (Combinatorial Number Theory and Additive Group Theory. Combinatorial Number Theory and Additive Group Theory, Adv. Courses Math. (2009), CRM Barcelona, Birkhäuser Verlag: CRM Barcelona, Birkhäuser Verlag Basel), 241-252 · Zbl 1214.11018 |
| [94] | Gao, W.; Hamidoune, Y. O.; Wang, G., Distinct length modular zero-sum subsequences: a proof of Graham’s conjecture, J. Number Theory, 130, 1425-1431 (2010) · Zbl 1203.11015 |
| [95] | Hamidoune, Y. O., Extensions of the Scherk-Kemperman theorem, J. Combin. Theory Ser. A, 117, 974-980 (2010) · Zbl 1235.05150 |
| [96] | Cilleruelo, J.; Hamidoune, Y. O.; Serra, O., Addition theorems in acyclic semigroups, (Additive Number Theory (2010), Springer: Springer New York), 99-104 · Zbl 1257.11092 |
| [97] | Hamidoune, Y. O.; da Silva, I. P., Distinct matroid base weights and additive theory, (Additive Number Theory (2010), Springer: Springer New York), 145-151 · Zbl 1259.11095 |
| [99] | Hamidoune, Y. O.; Rué, J., A lower bound for the size of a Minkowski sum of dilates, Combin. Probab. Comput., 20, 249-256 (2011) · Zbl 1231.11013 |
| [100] | Hamidoune, Y. O., A structure theory for small sum subsets, Acta Arith., 147, 303-327 (2011) · Zbl 1242.11073 |
| [101] | Hamidoune, Y. O.; Lladó, A.; López, S. C., Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors, J. Graph Theory, 67, 124-138 (2011) · Zbl 1217.05121 |
| [102] | Hamidoune, Y. O., Counting certain pairings in arbitrary groups, Combin. Probab. Comput., 20, 855-865 (2011) · Zbl 1238.20060 |
| [105] | Girard, B.; Griffiths, S.; Hamidoune, Y. O., \(k\)-sums in abelian groups, Combin. Probab. Comput., 21, 582-596 (2012) · Zbl 1247.05267 |
| [106] | Hamidoune, Y. O.; Lladó, A.; López, S. C., On vosperian and superconnected vertex-transitive digraphs, Graphs Combin., 29, 241-251 (2013) · Zbl 1263.05039 |
| [107] | Balandraud, É.; Girard, B.; Griffiths, S.; Hamidoune, Y. O., Subset sums in abelian groups, European. J. Combin., 34, 8, 1269-1286 (2013) · Zbl 1364.11026 |
| [108] | Hamidoune, Y. O.; López, S.; Plagne, A., Large restricted sumsets in general abelian groups, European. J. Combin., 34, 8, 1348-1364 (2013) · Zbl 1371.11025 |
| [110] | Bah, A. O., Les dames du désert, Jeux et Stratégies, 27, 46-48 (1984) |
| [111] | Diagana, T., Remembering Yahya Ould Hamidoune, Notices Amer. Math. Soc., 59, 827 (2012) · Zbl 1284.01057 |
| [112] | Plagne, A., Yahya ould Hamidoune, grand Mauritanien, homme singulier, mathématicien d’exception, Gaz. Math., 129, 123-129 (2011) · Zbl 1243.01018 |
| [113] | Plagne, A., Yahya Ould Hamidoune: the Mauritanian mathematician: 1948-11 March 2011, Combin. Probab. Comput., 20, 641-645 (2011) · Zbl 1227.01038 |
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