A tight bound on the length of odd cycles in the incompatibility graph of a non-C1P matrix
β Scribed by Mehrnoush Malekesmaeili; Cedric Chauve; Tamon Stephen
- Book ID
- 116577146
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 296 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0020-0190
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π SIMILAR VOLUMES
It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It
Let G be a maximal planar graph with p vertices, and let Ck(G) denote the number of cycles of length k in G. We first present tight bounds for C,(G) and C,(G) in terms of p. We then give bounds for Ck(G) when 5 5 k 5 p , and consider in particular bounds for C,(G), in terms of p. Some conjectures an
## Abstract Let __p__ and __C__~4~ (__G__) be the number of vertices and the number of 4βcycles of a maximal planar graph __G__, respectively. Hakimi and Schmeichel characterized those graphs __G__ for which __C__~4~ (__G__) = 1/2(__p__^2^ + 3__p__ β 22). This characterization is correct if __p__ β₯