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Comparability graphs and a new matroid. (English) Zbl 0352.05023


MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
05C99 Graph theory
06A06 Partial orders, general
Full Text: DOI

Online Encyclopedia of Integer Sequences:

Jordan-Polya numbers: products of factorial numbers A000142.

References:

[1] Aigner, M., Graphs and partial orderings, Monatsh. Math., 73, 385-396 (1969) · Zbl 0184.27502
[2] Aigner, M., Graphs and binary relations, (The Many Facets of Graph Theory. The Many Facets of Graph Theory, Lecture Notes in Mathematics, Vol. 110 (1969), Springer-Verlag: Springer-Verlag Berlin), 1-21 · Zbl 0186.27504
[3] Aigner, M.; Prins, G., Uniquely partially orderable graphs, J. London Math. Soc., 3, No. 2, 260-266 (1971) · Zbl 0214.51601
[4] Aigner, M.; Prins, G., Segment-preserving maps of partial orders, Trans. Amer. Math. Soc., 166, 351-360 (1972) · Zbl 0275.06002
[5] Berge, C., (Graphs and Hypergraphs (1973), North-Holland: North-Holland Amsterdam), Chap. 16 · Zbl 0483.05029
[6] Dushnik, B.; Miller, E. W., Partially ordered sets, Amer. J. Math., 63, 600-610 (1941) · Zbl 0025.31002
[7] Eilenberg, S., (Automata, Languages and Machines, Vol. A (1974), Academic Press: Academic Press New York) · Zbl 0317.94045
[8] Even, S.; Pnueli, A.; Lempel, A., Permutation graphs and transitive graphs, J. Assoc. Comput. Mach., 19, 400-410 (1972) · Zbl 0251.05113
[9] Fishburn, P., An interval graph is not a comparability graph, J. Combinatorial Theory, 8, 442-443 (1970) · Zbl 0183.28602
[10] Fishburn, P., (Utility Theory for Decision Making (1970), Wiley: Wiley New York), Chap. 1 · Zbl 0213.46202
[11] Gallai, T., Transitiv orientierbare Graphen, Acta Math. Acad. Sci. Hung., 18, 25-66 (1967) · Zbl 0153.26002
[12] Gavril, F., Algorithms for minimum coloring, maximum clique, minimum covering by cliques and maximum independent set of a chordal graph, SIAM J. Comp., 1, 180-187 (1972) · Zbl 0227.05116
[13] Ghouila-Houri, A., Caractérisation des graphes nonorientés dont on peut orienter les arêtes de manière à obtenir le graphe d’une relation d’ordre, C. R. Acad. Sci. Paris, 254, 1370-1371 (1962) · Zbl 0105.35503
[14] Ghouila-Houri, A., Flot et tensions dans un graphe, Ann. Scient. École Norm. Sup., 81, 207-265 (1964) · Zbl 0178.57603
[15] Gilmore, P. C.; Hoffman, A. J., A characterization of comparability graphs and of interval graphs, Canad. J. Math., 16, 539-548 (1964) · Zbl 0121.26003
[16] Golumbic, M. C., An infinite class of superperfect noncomparability graphs, IBM Research, RC 5064 (October, 1974)
[17] Golumbic, M. C., Comparability graphs and a new matroid, (extended abstract), (Proc Alg. Aspects of Comb. (January, 1975), Univ. of Toronto) · Zbl 0365.05025
[18] Hedetniemi, S. T., Graphs of (0, 1)-matrices, (Recent Trends in Graph Theory. Recent Trends in Graph Theory, Lecture Notes in Mathematics, Vol. 186 (1971), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0217.31206
[19] Hedetniemi, S. T.; Slater, P. J., Line graphs of triangleless graphs and interated clique graphs, (Graph Theory and Applications. Graph Theory and Applications, Lecture Notes in Mathematics, Vol. 303 (1972), Springer-Verlag: Springer-Verlag Berlin), 139-147 · Zbl 0255.05121
[20] Lekkerkerker, C. G.; Boland, J. Ch, Representation of a finite graph by a set of intervals on the real line, Fund. Math., 51, 45-64 (1962) · Zbl 0105.17501
[21] Pnueli, A.; Lempel, A.; Even, S., Transitive orientation of graphs and identification of permutation graphs, Canad. J. Math., 23, 160-175 (1971) · Zbl 0204.24604
[22] Roberts, F. S., Indifference graphs, (Harary, F., Proof Techniques in Graph Theory (1969), Academic Press: Academic Press New York), 139-146 · Zbl 0193.24205
[23] Rose, D. J., Triangulated graphs and the elimination process, J. Math. Anal. Appl., 32, 597-609 (1970) · Zbl 0216.02602
[24] Sharp, H., Enumeration of vacuously transitive relations, Discrete Math., 4, 185-196 (1973) · Zbl 0252.05003
[25] Shevrin, L. N.; Filippov, N. D., Partially ordered sets and their comparability graphs, Siberian Math. J., 11, 497-509 (1970) · Zbl 0214.23303
[26] Tucker, A., The strong perfect graph conjecture and an application to a municipal routing problem, (Graph Theory and Applications. Graph Theory and Applications, Lecture Notes in Mathematics, Vol. 303 (1972), Springer-Verlag: Springer-Verlag Berlin), 297-303 · Zbl 0247.05117
[27] Wilson, R. J., An introduction to matroid theory, Amer. Math. Monthyly, 80, 500-525 (1973) · Zbl 0275.05018
[28] Wolk, E. S., A note on the comparability graph of a tree, (Proc. Amer. Math. Soc., 16 (1965)), 17-20 · Zbl 0137.18105
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