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Smallest regular graphs without near 1-factors

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Gary Chartrand ,
Sergio Ruiz  and
Curtiss E. Wall
Gary Chartrand
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008, U.S.A.
Sergio Ruiz
Affiliation:
Office of Courseware Development, Norfolk Public Schools, Norfolk, Virginia 23508, U.S.A.
Curtiss E. Wall
Affiliation:
Instituto de Matemáticas, Universided Católica de Valparaíso, Valparaíso, Chile
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Abstract

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A near 1-factor of a graph of order 2n ≧ 4 is a subgraph isomorphic to (n − 2) K2 ∪ P3 ∪ K1. Wallis determined, for each r ≥ 3, the order of a smallest r-regular graph of even order without a 1-factor; while for each r ≧ 3, Chartrand, Goldsmith and Schuster determined the order of a smallest r-regular, (r − 2)-edge-connected graph of even order without a 1-factor. These results are extended to graphs without near 1-factors. It is known that every connected, cubic graph with less than six bridges has a near 1-factor. The order of a smallest connected, cubic graph with exactly six bridges and no near 1-factor is determined.

MSC classification

Secondary: 05C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 193 - 210
Copyright
Copyright © Australian Mathematical Society 1986

References

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