Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777088 | Electronic Notes in Discrete Mathematics | 2017 | 5 Pages |
Abstract
As applications, we prove new bounds on the number of independent sets and matchings of a given size in regular graphs. For large enough graphs and almost all sizes, the bounds are tight and confirm the Upper Matching Conjecture of Friedland, Krop, and Markström, and a conjecture of Kahn on independent sets for a wide range of parameters. Additionally we prove tight bounds on the number of q-colorings of cubic graphs with a given number of monochromatic edges, and tight bounds on the number of independent sets of a given size in cubic graphs of girth at least 5.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ewan Davies, Matthew Jenssen, Barnaby Roberts, Will Perkins,