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SEMIREGULAR FACTORIZATIONS OF REGULAR MULTIGRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  13 July 2010

Michael N. Ferencak  and
Anthony J. W. Hilton
Michael N. Ferencak
Affiliation:
Department of Mathematics, University of Pittsburgh at Johnstown, Johnstown, Pennsylvania 15904, U.S.A. (email: ferencak@pitt.edu)
Anthony J. W. Hilton
Affiliation:
Department of Mathematics, University of Reading, Whiteknights, Reading RG6 6AX, U.K.
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Abstract

An (r,r+1)-factor of a graph G is a spanning subgraph H such that dH(v)∈{r,r+1} for all vertices v∈𝒱(G). If G is expressed as the union of edge-disjoint (r,r+1)-factors, then this expression is an (r,r+1)-factorization of G. Let μ(r) be the smallest integer with the property that if G is a regular loopless multigraph of degree d with d≥μ(r), then G has an (r,r+1)-factorization. It is shown that if r is even. The proof employs a novel list-coloring approach. Together with known results, this shows that μ(r)=r2+1 if r is odd and if r is even.

MSC classification

Secondary: 05C70: Factorization, matching, partitioning, covering and packing 05C15: Coloring of graphs and hypergraphs
Type
Research Article
Information
Mathematika , Volume 56 , Issue 2 , July 2010 , pp. 357 - 362
Copyright
Copyright © University College London 2010

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