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On an Algorithm for Comparing the Chromatic Symmetric Functions of Trees
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abstract
It is a long-standing question of Stanley whether or not the chromatic symmetric function (CSF) distinguishes unrooted trees. Previously, the best computational result, due to Russell, proved that it distinguishes all trees with at most $25$ vertices. In this paper, we present a novel probabilistic algorithm which may be used to check more efficiently that the CSF distinguishes a set of trees. Applying it, we verify that the CSF distinguishes all trees with up to $29$ vertices.
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Cited by 1 Pith paper
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On Calculating the Chromatic Symmetric Function
The paper defines route operations that relate chromatic symmetric functions of graphs, proves forest graphs form a basis for symmetric functions by a combinatorial argument, and derives a subgraph-counting formula fo...
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