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A MINIMUM DEGREE CONDITION FOR FRACTIONAL ID-[a,b]-FACTOR-CRITICAL GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  07 February 2012

SIZHONG ZHOU ,
ZHIREN SUN  and
HONGXIA LIU
SIZHONG ZHOU*
Affiliation:
School of Mathematics and Physics, Jiangsu University of Science and Technology, Mengxi Road 2, Zhenjiang, Jiangsu 212003, PR China (email: zsz_cumt@163.com)
ZHIREN SUN
Affiliation:
School of Computer Science, Nanjing Normal University, Nanjing, Jiangsu 210046, PR China
HONGXIA LIU
Affiliation:
School of Mathematics and Informational Science, Yantai University, Yantai, Shandong 264005, PR China
*
✉For correspondence; e-mail: zsz_cumt@163.com
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Abstract

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Let G be a graph of order n, and let a and b be two integers with 1≤a≤b. Let h:E(G)→[0,1] be a function. If a≤∑ e∋xh(e)≤b holds for any x∈V (G), then we call G[Fh] a fractional [a,b] -factor of G with indicator function h, where Fh ={e∈E(G):h(e)>0}. A graph G is fractional independent-set-deletable [a,b] -factor-critical (in short, fractional ID-[a,b] -factor-critical) if G−I has a fractional [a,b] -factor for every independent set I of G. In this paper, it is proved that if n≥((a+2b)(a+b−2)+1 )/b and δ(G)≥((a+b)n )/(a+2b ) , then G is fractional ID-[a,b] -factor-critical. This result is best possible in some sense, and it is an extension of Chang, Liu and Zhu’s previous result.

Keywords

graphminimum degreeindependent setfractional [a,b]-factorfractional ID-[a,b]-factor-critical graph

MSC classification

Secondary: 05C70: Factorization, matching, partitioning, covering and packing
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 177 - 183
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

This research was supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (10KJB110003), Jiangsu University of Science and Technology (2010SL101J) and Shandong Province Higher Educational Science and Technology Program (J10LA14), and was sponsored by the Qing Lan Project of Jiangsu Province.

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