A New Method for Enumerating Independent Sets of a Fixed Size in General Graphs

作者：Alexander James^*; Mink Tim

来源：Journal of Graph Theory, 2016, 81(1): 57-72.

DOI：10.1002/jgt.21861

• independent sets
• minimum degree
• cliques
• subgraph enumeration
• extremal graph theory
• regular graphs
• Moore graphs

We develop a new method for enumerating independent sets of a fixed size in general graphs, and we use this method to show that a conjecture of Engbers and Galvin [7] holds for all but finitely many graphs. We also use our method to prove special cases of a conjecture of Kahn [13]. In addition, we show that our method is particularly useful for computing the number of independent sets of small sizes in general regular graphs and Moore graphs, and we argue that it can be used in many other cases when dealing with graphs that have numerous structural restrictions.

• 出版日期2016-1