On degree anti-Ramsey numbers

Shoni Gilboa, Dan Hefetz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The degree anti-Ramsey number ARd(H) of a graph H is the smallest integer k for which there exists a graph G with maximum degree at most k such that any proper edge colouring of G yields a rainbow copy of H. In this paper we prove a general upper bound on degree anti-Ramsey numbers, determine the precise value of the degree anti-Ramsey number of any forest, and prove an upper bound on the degree anti-Ramsey numbers of cycles of any length which is best possible up to a multiplicative factor of 2. Our proofs involve a variety of tools, including a classical result of Bollobás concerning cross intersecting families and a topological version of Hall's Theorem due to Aharoni, Berger and Meshulam.

Original languageEnglish
Pages (from-to)31-41
Number of pages11
JournalEuropean Journal of Combinatorics
Volume60
DOIs
StatePublished - 1 Feb 2017

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