A New Method for Enumerating Independent Sets of a Fixed Size in General Graphs |
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Authors: | James Alexander Tim Mink |
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Institution: | 1. DEPARTMENT OF MATHEMATICAL SCIENCES, UNIVERSITY OF DELAWARE, NEWARK, DE;2. DEPARTMENT OF MATHEMATICS, MONTCLAIR STATE UNIVERSITY, MONTCLAIR, NJ |
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Abstract: | 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. |
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Keywords: | independent sets minimum degree cliques subgraph enumeration extremal graph theory regular graphs Moore graphs |
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