scholarly journals A characterization of maximal non-k-factor-critical graphs

2007 ◽  
Vol 307 (1) ◽  
pp. 108-114 ◽  
Author(s):  
N. Ananchuen ◽  
L. Caccetta ◽  
W. Ananchuen
Keyword(s):  
Critical Graphs ◽  
K Factor

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

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

(2,k)-Factor-Critical Graphs and Toughness

1999 ◽  
Vol 15 (2) ◽  
pp. 137-142 ◽  
Author(s):  
Mao-Cheng Cai ◽  
Odile Favaron ◽  
Hao Li
Keyword(s):  
Critical Graphs ◽  
K Factor

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

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.

scholarly journals Face-Degree Bounds for Planar Critical Graphs

10.37236/5895 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Ligang Jin ◽  
Yingli Kang ◽  
Eckhard Steffen
Keyword(s):  
Planar Graph ◽  
Chromatic Number ◽  
Planar Graphs ◽  
Maximum Degree ◽  
Upper Bounds ◽  
Partial Characterization ◽  
Critical Graphs ◽  
Degree Bounds

The only remaining case of a well known conjecture of Vizing states that there is no planar graph with maximum degree 6 and edge chromatic number 7. We introduce parameters for planar graphs,  based on the degrees of the faces, and study the question whether there are upper bounds for these parameters for planar edge-chromatic critical graphs. Our results provide upper bounds on these parameters for smallest counterexamples to Vizing's conjecture, thus providing a partial characterization of such graphs, if they exist.For $k \leq 5$ the results give insights into the structure of planar edge-chromatic critical graphs.

scholarly journals A constructive characterization of total domination vertex critical graphs

2009 ◽  
Vol 309 (4) ◽  
pp. 991-996 ◽  
Author(s):  
Chunxiang Wang ◽  
Zhiquan Hu ◽  
Xiangwen Li
Keyword(s):  
Total Domination ◽  
Critical Graphs

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
Sign in / Sign up

Export Citation Format

Share Document