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NEIGHBOURHOODS OF INDEPENDENT SETS FOR (a,b,k)-CRITICAL GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  01 April 2008

SIZHONG ZHOU  and
YANG XU
SIZHONG ZHOU*
Affiliation:
School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, People’s Republic of China (email: [email protected])
YANG XU
Affiliation:
Department of Mathematics, Qingdao Agricultural University, Qingdao, Shandong 266109, People’s Republic of China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Let G be a graph of order n. Let a, b and k be nonnegative integers such that 1≤a≤b. A graph G is called an (a,b,k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a,b]-factor. We provide a sufficient condition for a graph to be (a,b,k)-critical that extends a well-known sufficient condition for the existence of a k-factor.

Keywords

graphminimum degreeneighbourhood[a,b]-factor(a,b,k)-critical graph

MSC classification

Secondary: 05C70: Factorization, matching, partitioning, covering and packing
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 2 , April 2008 , pp. 277 - 283
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

This research was supported by Jiangsu Provincial Educational Department (07KJD110048).

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