Ramsey numbers of squares of paths

Allen, Peter

(2015) Ramsey numbers of squares of paths. In: European Conference on Combinatorics, Graph Theory and Applications, 2015-08-31 - 2015-09-04, Bergen,Norway,NOR.

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The Ramsey number R(G;H) has been actively studied for the past 40 years, and it was determined for a large family of pairs (G;H) of graphs. The Ramsey number of paths was determined very early on, but surprisingly very little is known about the Ramsey number for the powers of paths. The r-th power Pr n of a path on n vertices is obtained by joining any two vertices with distance at most r. We determine the exact value of R(P2 n; P2 n) for n large and discuss some related questions.

Item Type	Conference or Workshop Item (Paper)
Keywords	Ramsey theory,regularity method,stability,powers of graphs
Departments	Mathematics
Date Deposited	09 Dec 2015 14:49
URI	https://researchonline.lse.ac.uk/id/eprint/64639