TOUGHNESS AND DEGREE CONDITION FOR FRACTIONAL ID-k-FACTOR-CRITICAL GRAPHS

YUAN YUAN; ZHIREN SUN

doi:10.1142/s1793830914500268

TOUGHNESS AND DEGREE CONDITION FOR FRACTIONAL ID-k-FACTOR-CRITICAL GRAPHS

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830914500268 ◽

2014 ◽

Vol 06 (02) ◽

pp. 1450026

Author(s):

YUAN YUAN ◽

ZHIREN SUN

Keyword(s):

Independent Set ◽

Critical Graphs ◽

Degree Condition ◽

K Factor

A graph G is fractional independent-set-deletable k-factor-critical if G-I has a fractional k-factor for every independent set I of G. In this paper, we prove that if |V(G)| ≥ k + 2, [Formula: see text] and t(G) ≥ k2 + 6k, then G is fractional ID-k-factor-critical.

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

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972711003467 ◽

2012 ◽

Vol 86 (2) ◽

pp. 177-183 ◽

Cited By ~ 2

Author(s):

SIZHONG ZHOU ◽

ZHIREN SUN ◽

HONGXIA LIU

Keyword(s):

Minimum Degree ◽

Independent Set ◽

Indicator Function ◽

Critical Graphs ◽

Degree Condition

AbstractLet 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.

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Neighbourhood conditions for fractional ID-[a, b]-factor-critical graphs

Publications de l Institut Mathematique ◽

10.2298/pim1715205y ◽

2017 ◽

Vol 101 (115) ◽

pp. 205-212

Author(s):

Yuan Yuan ◽

Zhiren Sun

Keyword(s):

Independent Set ◽

Critical Graphs ◽

K Factor

A graph G is fractional ID-[a, b]-factor-critical if G?I has a fractional [a, b]-factor for every independent set I of G. We extend a result of Zhou and Sun concerning fractional ID-k-factor-critical graphs.

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