Path-sequential labellings of cycles. (English) Zbl 0870.05063
Summary: We investigate labelling the vertices of the cycle of length \(n\) with the integers \(0,\dots, n-1\) in such a way that the \(n\) sums of \(k\) adjacent integers are sequential. We show that this is impossible for both \(n\) and \(k\) even, possible for \(n\) even and \(k\) odd, and that it is possible for many cases where \(n\) is odd. We conjecture that it is always possible when \(n\) is odd.
References:
| [1] | Chung, F.; Diaconis, P.; Graham, R., Universal cycles for combinatorial structures, Discrete Math., 110, 43-59 (1992) · Zbl 0776.05001 |
| [2] | de Bruijn, N. G., A Combinatorial Problem, (Proc. Nederl. Akad. Wetensch., 49 (1946)), 758-764 · Zbl 0060.02701 |
| [3] | Gallian, J. A., A survey: recent results, conjectures, and open problems on labeling graphs, J. Graph Theory, 13, 491-504 (1989) · Zbl 0681.05064 |
| [4] | Graham, R. L.; Sloane, N. J.A., On additive bases and harmonious graphs, SIAM J. Algebraic Discrete Methods, 1, 382-404 (1980) · Zbl 0499.05049 |
| [5] | Hurlbert, G., (Ph. D. Thesis (1990), Rutgers University) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
