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Some results on an edge coloring problem of Folkman and Fulkerson
Luleå University of Technology.
2000 (English)In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 223, no 1-3, p. 13-25Article in journal (Refereed) Published
Abstract [en]

In 1968, Folkman and Fulkerson posed the following problem: Let G be a graph and let (n1,...,nt) be a sequence of positive integers. Does there exist a proper edge coloring of G with colors 1,2,...,t such that precisely ni edges receive color i, for each i=1,...,t? If such a coloring exists then the sequence (n1,...,nt) is called color-feasible for G. Some sufficient conditions for a sequence to be color-feasible for a bipartite graph where found by Folkman and Fulkerson, and de Werra. In this paper we give a generalization of their results for bipartite graphs. Furthermore, we find a set of color-feasible sequences for an arbitrary simple graph. In particular, we describe the set of all sequences which are color-feasible for a connected simple graph G with Δ(G)3, where every pair of vertices of degree at least 3 are non-adjacent.

Place, publisher, year, edition, pages
2000. Vol. 223, no 1-3, p. 13-25
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-14004DOI: 10.1016/S0012-365X(00)00061-3ISI: 000089332600002Local ID: d5400fb0-b04c-11db-840a-000ea68e967bOAI: oai:DiVA.org:ltu-14004DiVA, id: diva2:986958
Note

Validerad; 2000; 20070130 (kani)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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