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(1, 2)-Factorizations of General Eulerian Nearly Regular Graphs

Published online by Cambridge University Press:  12 September 2008

Roland Häggkvist  and
Anders Johansson
Roland Häggkvist
Affiliation:
Department of Mathematics, University of Umeå, S-901 87 Umeå, SwedenE-mail address:rolandh@biovax.umdc.umu.se, andersj@zeus.cs.umu.se
Anders Johansson
Affiliation:
Department of Mathematics, University of Umeå, S-901 87 Umeå, SwedenE-mail address:rolandh@biovax.umdc.umu.se, andersj@zeus.cs.umu.se
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Abstract

Every general graph with degrees 2k and 2k − 2, k ≥ 3, with zero or at least two vertices of degree 2k − 2 in each component, has a k-edge-colouring such that each monochromatic subgraph has degree 1 or 2 at every vertex.

In particular, if T is a triangle in a 6-regular general graph, there exists a 2-factorization of G such that each factor uses an edge in T if and only if T is non-separating.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 87 - 95
Copyright
Copyright © Cambridge University Press 1994

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References

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