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 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 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 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 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

scholarly journals On the Number of Sum-Free Triplets of Sets

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Igor Araujo ◽  
József Balogh ◽  
Ramon I. Garcia
Keyword(s):  
Abelian Group ◽  
Recent Result ◽  
Independent Sets ◽  
Regular Graphs ◽  
Simpler Method

We count the ordered sum-free triplets of subsets in the group $\mathbb{Z}/p\mathbb{Z}$, i.e., the triplets $(A,B,C)$ of sets $A,B,C \subset \mathbb{Z}/p\mathbb{Z}$ for which the equation $a+b=c$ has no solution with $a\in A$, $b \in B$ and $c \in C$. Our main theorem improves on a recent result by Semchankau, Shabanov, and Shkredov using a different and simpler method. Our proof relates previous results on the number of independent sets of regular graphs by Kahn; Perarnau and Perkins; and Csikvári to produce explicit estimates on smaller order terms. We also obtain estimates for the number of sum-free triplets of subsets in a general abelian group. 

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