s-Positivity of clawfree graphs

Prove that the chromatic symmetric function of every clawfree graph is s-positive, namely, that it has a nonnegative expansion in the Schur-function basis.

Background

The paper notes that incomparability graphs of (3+1)-free posets form a proper subclass of clawfree graphs. It describes the broader s-positivity assertion for clawfree graphs as a conjecture attributed to Stanley and Gasharov.

References

These incomparability graphs are a proper subclass of clawfree graphs, whose chromatic symmetric functions are also conjectured by Stanley (and Gasharov) to be s-positive [21], i.e., a non-negative linear expansion of Schur functions.

— A quantitative way to e-positivity of trees  (2503.09484 - Li, 12 Mar 2025) in Section 1, Introduction, page 1