Open Collections

Resolving Stanley's e-Positivity of Claw-Contractible-Free Graphs

Banff International Research Station for Mathematical Innovation and Discovery

In Stanley's seminal 1995 paper on the chromatic symmetric function, he stated that there was no known graph that was not contractible to the claw and whose chromatic symmetric function was not e-positive, namely, not a positive linear combination of elementary symmetric functions. We resolve this by giving infinite families of graphs that are not contractible to the claw and whose chromatic symmetric functions are not e-positive. Moreover, one such family is additionally claw-free, thus establishing that the e-positivity of chromatic symmetric functions in general is not dependent on the claw.

Mathematics; Combinatorics; Group theory and generalizations

video/mp4

Author affiliation: University of British Columbia

2017-11-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63599

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/