Independence number and minimum degree for fractional ID-k-factor-critical graphs

2012 ◽  
Vol 84 (1-2) ◽  
pp. 71-76 ◽  
Author(s):  
Sizhong Zhou ◽  
Lan Xu ◽  
Zhiren Sun
Keyword(s):  
Minimum Degree ◽  
Independence Number ◽  
Critical Graphs ◽  
K Factor

scholarly journals Two sufficient conditions for fractional k-deleted graphs

2012 ◽  
Vol 20 (1) ◽  
pp. 265-274
Author(s):  
Xiangyang Lv
Keyword(s):  
Positive Integer ◽  
Minimum Degree ◽  
Independence Number ◽  
Sufficient Conditions ◽  
K Factor

Abstract Let G be a graph, and k a positive integer. A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if G - e has a fractional k-factor for each e ∈ 2 E(G). In this paper, we obtain some sufficient conditions for graphs to be fractional k-deleted graphs in terms of their minimum degree and independence number. Furthermore, we show the results are best possible in some sense

Remarks on Fractional ID-k-factor-critical Graphs

2019 ◽  
Vol 35 (2) ◽  
pp. 458-464 ◽  
Author(s):  
Si-zhong Zhou ◽  
Lan Xu ◽  
Zu-run Xu
Keyword(s):  
Critical Graphs ◽  
K Factor

On the maximum connective eccentricity index among k-connected graphs

2020 ◽  
pp. 2150002
Author(s):  
Fazal Hayat
Keyword(s):  
Minimum Degree ◽  
Independence Number ◽  
Connected Graphs ◽  
Eccentricity Index

The connective eccentricity index (CEI for short) of a graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the degree of [Formula: see text] and [Formula: see text] is the eccentricity of [Formula: see text] in [Formula: see text]. In this paper, we characterize the unique graphs with maximum CEI from three classes of graphs: the [Formula: see text]-vertex graphs with fixed connectivity and diameter, the [Formula: see text]-vertex graphs with fixed connectivity and independence number, and the [Formula: see text]-vertex graphs with fixed connectivity and minimum degree.

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

2012 ◽  
Vol 86 (2) ◽  
pp. 177-183 ◽  
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.

scholarly journals Triangle-Tilings in Graphs Without Large Independent Sets

2018 ◽  
Vol 27 (4) ◽  
pp. 449-474 ◽  
Author(s):  
JÓZSEF BALOGH ◽  
ANDREW McDOWELL ◽  
THEODORE MOLLA ◽  
RICHARD MYCROFT
Keyword(s):  
Minimum Degree ◽  
Independence Number ◽  
Independent Sets ◽  
Vertex Graph ◽  
Additional Assumptions

We study the minimum degree necessary to guarantee the existence of perfect and almost-perfect triangle-tilings in an n-vertex graph G with sublinear independence number. In this setting, we show that if δ(G) ≥ n/3 + o(n), then G has a triangle-tiling covering all but at most four vertices. Also, for every r ≥ 5, we asymptotically determine the minimum degree threshold for a perfect triangle-tiling under the additional assumptions that G is Kr-free and n is divisible by 3.

A conjecture on k-factor-critical and 3-γ-critical graphs

2010 ◽  
Vol 53 (5) ◽  
pp. 1385-1391 ◽  
Author(s):  
Tao Wang ◽  
QingLin Yu
Keyword(s):  
Critical Graphs ◽  
K Factor
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