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Four-Cycled Graphs with Topological Applications

✍ Scribed by Türker Bıyıkoğlu; Yusuf Civan

Publisher
Springer
Year
2011
Tongue
English
Weight
362 KB
Volume
16
Category
Article
ISSN
0218-0006

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📜 SIMILAR VOLUMES

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We investigate the values of t(n), the maximum number of edges in a graph with n vertices and not containing a four-cycle. Techniques for finding these are developed and the values of t(n) for all n up to 21 are obtained. All the corresponding extremal graphs are found.

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## Abstract We derive bounds for __f(v)__, the maximum number of edges in a graph on __v__ vertices that contains neither three‐cycles nor four‐cycles. Also, we give the exact value of __f(v)__ for all __v__ up to 24 and constructive lower bounds for all __v__ up to 200. © 1993 John Wiley & Sons, I

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We prove that every bipartite C 2' -free graph G contains a C 4free subgraph H with e(H) ! e(G)=(' À 1). The factor 1=(' À 1) is best possible. This implies that ex(n; C 2' ) 2(' À 1)ex(n; fC 4 ; C 2' g), which settles a special case of a conjecture of Erdo ˝s and Simonovits.

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It is shown that there is a graph 4 with n vertices and at least n ' "edges such that it contains neither Ws nor X2 3 , but every subgraph with 2n4'3(logn)Z edges contains a vd, (n>n,). Moreover, the chromatic number of Y is at least no.'.