Remarks on Fractional ID-k-factor-critical Graphs

Zhou, Sizhong; Xu, Lan; Xu, Zurun

doi:10.1007/s10255-019-0818-6

Cited by 12 publications

(3 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many results on the binding number conditions for the existence of graph factors were acquired by Nam [12], Plummer and Saito [13], Zhou [17,18], Robertshaw and Woodall [14]. Some results on factor deleted graphs see [3,4,19], and some results on factor critical graphs see [2,5,15,16,21]. Many authors [1,6,10,11,20,22,23] studied the existence of path factors in graphs.…”

Section: Introductionmentioning

confidence: 99%

Remarks on path factors in graphs

Zhou

2020

RAIRO-Oper. Res.

View full text Add to dashboard Cite

A spanning subgraph of a graph is defined as a path factor of the graph if its component are paths. A $P_{\geq n}$-factor means a path factor with each component having at least $n$ vertices. A graph $G$ is defined as a $(P_{\geq n},m)$-factor deleted graph if $G-E'$ has a $P_{\geq n}$-factor for every $E'\subseteq E(G)$ with $|E'|=m$. A graph $G$ is defined as a $(P_{\geq n},k)$-factor critical graph if after deleting any $k$ vertices of $G$ the remaining graph of $G$ admits a $P_{\geq n}$-factor. In this paper, we demonstrate that (\romannumeral1) a graph $G$ is $(P_{\geq3},m)$-factor deleted if $\kappa(G)\geq2m+1$ and $bind(G)\geq\frac{3}{2}-\frac{1}{4m+4}$; (\romannumeral2) a graph $G$ is $(P_{\geq3},k)$-factor critical if $\kappa(G)\geq k+2$ and $bind(G)\geq\frac{5+k}{4}$.

show abstract

Section: Introductionmentioning

confidence: 99%

Remarks on path factors in graphs

Zhou

2020

RAIRO-Oper. Res.

View full text Add to dashboard Cite

show abstract

“…The concept of fractional (g, f , n , m)critical deleted graph can be regarded as a combination of fractional (g, f , n )-critical graph and fractional (g, f , m)-deleted graph, i.e., a graph G is fractional (g, f , n , m)-critical deleted if after n vertices are deleted from G, the rest of the graph is a fractional (g, f , m)-deleted graph. For some recent advances on the existence of a fractional factor in various settings, we can refer to Gao et al [7][8][9][10]12], Liu et al [18], and Zhou et al [34,35,37,[39][40][41][42][43].…”

Section: Background and Conceptsmentioning

confidence: 99%

Parameters and fractional factors in different settings

Gao

Guirao

2019

J Inequal Appl

View full text Add to dashboard Cite

In computer networks, the feasibility of data transmission can be measured in terms of fractional factor model, and specifically the framework of fractional critical deleted graph can express the setting when certain sites and channels are unavailable at a special time. We study the relationship between some parameters in graphs and the existence of fractional (g, f )-factor in various settings here. Our main contributions are three-fold: first, a connectivity condition for a graph to be fractional (g, f , n , m)-critical deleted is determined; second, the relationship between independence number and fractional ID-(g, f , m)-deleted graphs is studied; third, an isolated toughness bound for fractional (g, f )-factors is given in balanced bipartite graph setting. Furthermore, by showing counterexamples we explain that bounds for parameters are tight in some sense, and corresponding conditions in all fractional factor settings are discussed as well. Finally, two open problems are proposed for future research. MSC: 05C70

show abstract

“…Some other results related to factors [2][3][4][5][6][7][8][9] and fractional factors [10][11][12][13][14][15][16][17][18] of graphs were obtained by many authors. A graph G is called a fractional (a, b, k)-critical covered graph if after removing any k vertices of G, the resulting graph of G is a fractional [a, b]-covered graph, which is first defined by Zhou, Xu and Sun [19].…”

Section: Theorem 1 ( [1]mentioning

confidence: 99%