On colour critical graphs

2006 ◽  
pp. 390-401
Author(s):  
Horst Sachs
Keyword(s):  
Critical Graphs

scholarly journals Improvement on the Crossing Number of Crossing-Critical Graphs

2020 ◽  
Author(s):  
János Barát ◽  
Géza Tóth
Keyword(s):  
Crossing Number ◽  
Critical Graphs ◽  
Minimum Number ◽  
Edge Crossings

AbstractThe crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. A graph G is k-crossing-critical if its crossing number is at least k, but if we remove any edge of G, its crossing number drops below k. There are examples of k-crossing-critical graphs that do not have drawings with exactly k crossings. Richter and Thomassen proved in 1993 that if G is k-crossing-critical, then its crossing number is at most $$2.5\, k+16$$ 2.5 k + 16 . We improve this bound to $$2k+8\sqrt{k}+47$$ 2 k + 8 k + 47 .

scholarly journals Counting Critical Subgraphs in k-Critical Graphs

COMBINATORICA ◽  
2021 ◽  
Author(s):  
Jie Ma ◽  
Tianchi Yang
Keyword(s):  
Critical Graphs

Excluding induced subgraphs: Critical graphs

2010 ◽  
Vol 38 (1-2) ◽  
pp. 100-120 ◽  
Author(s):  
József Balogh ◽  
Jane Butterfield
Keyword(s):  
Induced Subgraphs ◽  
Critical Graphs

scholarly journals Subcubic Edge-Chromatic Critical Graphs Have Many Edges

2017 ◽  
Vol 86 (1) ◽  
pp. 122-136 ◽  
Author(s):  
Daniel W. Cranston ◽  
Landon Rabern
Keyword(s):  
Critical Graphs

scholarly journals On the existence problem of the total domination vertex critical graphs

2011 ◽  
Vol 159 (1) ◽  
pp. 46-52 ◽  
Author(s):  
Moo Young Sohn ◽  
Dongseok Kim ◽  
Young Soo Kwon ◽  
Jaeun Lee
Keyword(s):  
Existence Problem ◽  
Total Domination ◽  
Critical Graphs

scholarly journals Some results on the independence number of connected domination critical graphs

2018 ◽  
Vol 15 (2) ◽  
pp. 190-196 ◽  
Author(s):  
P. Kaemawichanurat ◽  
T. Jiarasuksakun
Keyword(s):  
Independence Number ◽  
Critical Graphs

On all fractional (a, b, k)-critical graphs

2014 ◽  
Vol 30 (4) ◽  
pp. 696-702 ◽  
Author(s):  
Si Zhong Zhou ◽  
Zhi Ren Sun
Keyword(s):  
Critical Graphs

Smallest $$C_{2l+1}$$-Critical Graphs of Odd-Girth $$2k+1$$

2020 ◽  
pp. 184-196
Author(s):  
Laurent Beaudou ◽  
Florent Foucaud ◽  
Reza Naserasr
Keyword(s):  
Critical Graphs

k-Extendable Graphs and n-Factor-Critical Graphs

2009 ◽  
pp. 209-249 ◽  
Author(s):  
Qinglin Roger Yu ◽  
Guizhen Liu
Keyword(s):  
Critical Graphs

scholarly journals Spectral strengthening of a theorem on transversal critical graphs

2022 ◽  
Vol 345 (3) ◽  
pp. 112717
Author(s):  
Muhuo Liu ◽  
Xiaofeng Gu
Keyword(s):  
Critical Graphs
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