INDEPENDENCE NUMBER, CONNECTIVITY AND ALL FRACTIONAL (a, b, k)-CRITICAL GRAPHS

被引：20

作者：

Yuan, Yuan ^{[1
]}

Hao, Rong-Xia ^{[1
]}

机构：

[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China

来源：

DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2019年 / 39卷 / 01期

基金：

中国国家自然科学基金;

关键词：

independence number; connectivity; fractional; a; b]-factor; (a; b; k)-critical graph; all fractional (a; SIMPLIFIED EXISTENCE THEOREMS; F)-FACTORS; (G;

D O I：

10.7151/dmgt.2075

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a graph and a, b and k be nonnegative integers with 1 <= a <= b. A graph G is defined as all fractional (a, b, k)-critical if after deleting any k vertices of G, the remaining graph has all fractional [a, b]-factors. In this paper, we prove that if kappa(G) >= max {(b+1)(2)+2k/2, (b+1)(2)alpha(G)+4ak/4a}, then G is all fractional (a, b, k)-critical. If k = 0, we improve the result given in [Filomat 29 (2015) 757-761]. Moreover, we show that this result is best possible in some sense.

引用

页码：183 / 190

页数：8

共 14 条

[1] SIMPLIFIED EXISTENCE THEOREMS FOR (G,F)-FACTORS [J].

ANSTEE, RP .

DISCRETE APPLIED MATHEMATICS, 1990, 27 (1-2) :29-38

[2] Independence Number, Connectivity and Fractional (g, f)-Factors in Graphs [J].

Bian, Qiuju ;

Zhou, Sizhong .

FILOMAT, 2015, 29 (04) :757-761

[3] Some remarks about factors of graphs [J].

Correa, Jose R. ;

Matamala, Martin .

JOURNAL OF GRAPH THEORY, 2008, 57 (04) :265-274

[4] Fractional (g, f)-factors of graphs [J].

Liu, GZ ;

Zhang, LJ .

ACTA MATHEMATICA SCIENTIA, 2001, 21 (04) :541-545

[5]

Liu SL, 2009, ARS COMBINATORIA, V93, P305

[6] Simplified existence theorems on all fractional [a, b]-factors [J].

Lu, Hongliang .

DISCRETE APPLIED MATHEMATICS, 2013, 161 (13-14) :2075-2078

[7] A characterization of graphs having all (g,f)-factors [J].

Niessen, T .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1998, 72 (01) :152-156

[8] INDEPENDENCE NUMBER, CONNECTIVITY, AND R-FACTORS [J].

NISHIMURA, T .

JOURNAL OF GRAPH THEORY, 1989, 13 (01) :63-69

[9] On all fractional (a, b, k)-critical graphs [J].

Zhou, Si Zhong ;

Sun, Zhi Ren .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2014, 30 (04) :696-702

[10] SOME RESULTS ABOUT COMPONENT FACTORS IN GRAPHS [J].

Zhou, Sizhong .

RAIRO-OPERATIONS RESEARCH, 2019, 53 (03) :723-730

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