Uncover Low Degree Vertices and Minimise the Mess: Independent Sets in Random Regular Graphs

2007 ◽  
pp. 56-66 ◽  
Author(s):  
William Duckworth ◽  
Michele Zito
Keyword(s):  
Independent Sets ◽  
Regular Graphs ◽  
Low Degree

scholarly journals Minimizing the number of independent sets in triangle-free regular graphs

2018 ◽  
Vol 341 (3) ◽  
pp. 793-800 ◽  
Author(s):  
Jonathan Cutler ◽  
A.J. Radcliffe
Keyword(s):  
Independent Sets ◽  
Regular Graphs

scholarly journals Large 2-Independent Sets of Regular Graphs

2003 ◽  
Vol 78 ◽  
pp. 223-235 ◽  
Author(s):  
W. Duckworth ◽  
M. Zito
Keyword(s):  
Independent Sets ◽  
Regular Graphs

scholarly journals Independent sets in {claw,K4}-free 4-regular graphs

2014 ◽  
Vol 332 ◽  
pp. 40-44 ◽  
Author(s):  
Liying Kang ◽  
Dingguo Wang ◽  
Erfang Shan
Keyword(s):  
Independent Sets ◽  
Regular Graphs

scholarly journals Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ≤ 14 Players

Games ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 12
Author(s):  
Hendrik Richter
Keyword(s):  
Regular Graph ◽  
Good Predictor ◽  
Computational Approach ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Regular Graphs ◽  
Weak Selection ◽  
Structure Coefficient ◽  
Low Degree ◽  
Emergence Of Cooperation

We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. In a computational approach using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with N ≤ 14 vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of a certain length is a good predictor for the values of the structure coefficient, and thus a tendency to favor cooperation. Another property of particularly cooperation-promoting regular graphs with a low degree is that they are structured to have blocks with clusters of mutants that are connected by cut vertices and/or hinge vertices.

scholarly journals Matchings and independent sets of a fixed size in regular graphs

2009 ◽  
Vol 116 (7) ◽  
pp. 1219-1227 ◽  
Author(s):  
Teena Carroll ◽  
David Galvin ◽  
Prasad Tetali
Keyword(s):  
Independent Sets ◽  
Regular Graphs ◽  
Fixed Size

scholarly journals An upper bound for the number of independent sets in regular graphs

2009 ◽  
Vol 309 (23-24) ◽  
pp. 6635-6640 ◽  
Author(s):  
David Galvin
Keyword(s):  
Upper Bound ◽  
Independent Sets ◽  
Regular Graphs

scholarly journals Independent sets in quasi-regular graphs

2006 ◽  
Vol 27 (7) ◽  
pp. 1206-1210 ◽  
Author(s):  
Alexander A. Sapozhenko
Keyword(s):  
Independent Sets ◽  
Regular Graphs

scholarly journals A Generalized Information-Theoretic Approach for Bounding the Number of Independent Sets in Bipartite Graphs

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 270
Author(s):  
Igal Sason
Keyword(s):  
Upper Bound ◽  
Independent Sets ◽  
Bipartite Graphs ◽  
Theoretic Approach ◽  
Regular Graphs ◽  
Proof Technique ◽  
Information Theoretic ◽  
Theoretic Proof ◽  
Information Theoretic Approach ◽  
General Graphs

This paper studies the problem of upper bounding the number of independent sets in a graph, expressed in terms of its degree distribution. For bipartite regular graphs, Kahn (2001) established a tight upper bound using an information-theoretic approach, and he also conjectured an upper bound for general graphs. His conjectured bound was recently proved by Sah et al. (2019), using different techniques not involving information theory. The main contribution of this work is the extension of Kahn’s information-theoretic proof technique to handle irregular bipartite graphs. In particular, when the bipartite graph is regular on one side, but may be irregular on the other, the extended entropy-based proof technique yields the same bound as was conjectured by Kahn (2001) and proved by Sah et al. (2019).

scholarly journals Large independent sets in random regular graphs

2009 ◽  
Vol 410 (50) ◽  
pp. 5236-5243 ◽  
Author(s):  
William Duckworth ◽  
Michele Zito
Keyword(s):  
Independent Sets ◽  
Regular Graphs
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