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On the number of (r,r+1)- factors in an (r,r+1)-factorization of a simple graph

✍ Scribed by A. J. W. Hilton

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
113 KB
Volume
60
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

For integers dβ‰₯0, sβ‰₯0, a (d, d+s)‐graph is a graph in which the degrees of all the vertices lie in the set {d, d+1, …, d+s}. For an integer rβ‰₯0, an (r, r+1)‐factor of a graph G is a spanning (r, r+1)‐subgraph of G. An (r, r+1)‐factorization of a graph G is the expression of G as the edge‐disjoint union of (r, r+1)‐factors. For integers r, sβ‰₯0, tβ‰₯1, let f(r, s, t) be the smallest integer such that, for each integer dβ‰₯f(r, s, t), each simple (d, d+s) ‐graph has an (r, r+1) ‐factorization with x (r, r+1) ‐factors for at least t different values of x. In this note we evaluate f(r, s, t). Β© 2009 Wiley Periodicals, Inc. J Graph Theory 60: 257‐268, 2009

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