Large Cliques in -Free Graphs

Dedicated to the memory of Paul Erdős

A graph is called -free if it contains no cycle of length four as an induced subgraph. We prove that if a -free graph has n vertices and at least edges then it has a complete subgraph of vertices, where depends only on . We also give estimates on and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of . The best value of is determined for chordal graphs.

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Received October 25, 1999

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ID="*" Supported by OTKA grant T029074.

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ID="**" Supported by TKI grant stochastics@TUB and by OTKA grant T026203.

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Gyárfás, A., Hubenko, A. & Solymosi, J. Large Cliques in -Free Graphs. Combinatorica 22, 269–274 (2002). https://doi.org/10.1007/s004930200012

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  • AMS Subject Classification (2000) Classes:  05C35