The Kneser chromatic function distinguishes trees

2024/09/30 by Yusaku Nishimura, Nishimura, Yusaku · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Machine Learning in Bioinformatics #Fractal and DNA sequence analysis #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2409.20478

Abstract

R.P. Stanley defined a invariant for graphs called the chromatic symmetric function and conjectured it is complete invariant for trees. Miezaki et al. generalised the chromatic symmetric function and defined the Kneser chromatic functions denoted by \X_K_ℕ,k\_k∈ℕ, and rephrase Stanley's conjecture that X_K_ℕ,1 is a complete invariant for trees. This paper shows X_K_ℕ,2 is a complete invariant for trees.

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