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Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Published online by Cambridge University Press:  02 February 2012

CARLOS HOPPEN ,
YOSHIHARU KOHAYAKAWA  and
HANNO LEFMANN
CARLOS HOPPEN
Affiliation:
Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Avenida Bento Gonçalves, 9500, 91509-900 Porto Alegre, Brazil (e-mail: [email protected])
YOSHIHARU KOHAYAKAWA
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, Brazil (e-mail: [email protected])
HANNO LEFMANN
Affiliation:
Fakultät für Informatik, Technische Universität Chemnitz, Straße der Nationen 62, D-09107 Chemnitz, Germany (e-mail: [email protected])
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Abstract

Let k and ℓ be positive integers. With a graph G, we associate the quantity ck,ℓ(G), the number of k-colourings of the edge set of G with no monochromatic matching of size ℓ. Consider the function ck,ℓ: given by ck,ℓ(n) = max {ck,ℓ(G): |V(G)| = n}, the maximum of ck,ℓ(G) over all graphs G on n vertices. In this paper, we determine ck,ℓ(n) and the corresponding extremal graphs for all large n and all fixed values of k and ℓ.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 1-2: Honouring the Memory of Richard H. Schelp , March 2012 , pp. 203 - 218
Copyright
Copyright © Cambridge University Press 2012

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