scholarly journals Critical graphs for the chromatic edge-stability number

2020 ◽  
Vol 343 (6) ◽  
pp. 111845
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Nazanin Movarraei
Keyword(s):  
Stability Number ◽  
Critical Graphs ◽  
Edge Stability

Nordhaus–Gaddum and other bounds for the chromatic edge-stability number

2020 ◽  
Vol 84 ◽  
pp. 103042 ◽  
Author(s):  
Saieed Akbari ◽  
Sandi Klavžar ◽  
Nazanin Movarraei ◽  
Mina Nahvi
Keyword(s):  
Stability Number ◽  
Edge Stability

STABILITY NUMBER AND MINIMUM DEGREE FOR (a, b, k)-CRITICAL GRAPHS

2013 ◽  
Vol 05 (04) ◽  
pp. 1350027
Author(s):  
SIZHONG ZHOU ◽  
YANG XU ◽  
JIANCHENG WU
Keyword(s):  
Minimum Degree ◽  
Sufficient Condition ◽  
Stability Number ◽  
Critical Graphs

In this paper, a sufficient condition for graphs to be (a, b, k)-critical graphs is given. This result is best possible in some sense, and it is an improvement of the previous result of Zhou, Xu and Zong.

On the Chromatic Edge Stability Number of Graphs

2018 ◽  
Vol 34 (6) ◽  
pp. 1539-1551 ◽  
Author(s):  
Arnfried Kemnitz ◽  
Massimiliano Marangio ◽  
Nazanin Movarraei
Keyword(s):  
Stability Number ◽  
Edge Stability

scholarly journals On the ρ-edge stability number of graphs

2019 ◽  
Author(s):  
Arnfried Kemnitz ◽  
Massimiliano Marangio
Keyword(s):  
Stability Number ◽  
Edge Stability

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 .

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

Shock formation induced by poloidal flow and its effects on the edge stability in tokamaks

2016 ◽  
Vol 23 (4) ◽  
pp. 042501 ◽  
Author(s):  
J. Seol ◽  
K. C. Shaing ◽  
A. Y. Aydemir
Keyword(s):  
Shock Formation ◽  
Edge Stability

scholarly journals A characterization of the weighted version of McEliece–Rodemich–Rumsey–Schrijver number based on convex quadratic programming

2015 ◽  
Vol 07 (04) ◽  
pp. 1550050
Author(s):  
Carlos J. Luz
Keyword(s):  
Quadratic Programming ◽  
Discrete Math ◽  
Convex Quadratic Programming ◽  
Stability Number ◽  
Weighted Version ◽  
Similar Characterization ◽  
Number Formula ◽  
Weighted Stability ◽  
Theta Number

For any graph [Formula: see text] Luz and Schrijver [A convex quadratic characterization of the Lovász theta number, SIAM J. Discrete Math. 19(2) (2005) 382–387] introduced a characterization of the Lovász number [Formula: see text] based on convex quadratic programming. A similar characterization is now established for the weighted version of the number [Formula: see text] independently introduced by McEliece, Rodemich, and Rumsey [The Lovász bound and some generalizations, J. Combin. Inform. Syst. Sci. 3 (1978) 134–152] and Schrijver [A Comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory 25(4) (1979) 425–429]. Also, a class of graphs for which the weighted version of [Formula: see text] coincides with the weighted stability number is characterized.

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
Sign in / Sign up

Export Citation Format

Share Document