All cycle-chords are e-positive

2024/05/02 by David G. L. Wang, Wang, David G. L. · 1 citation
Computer Science · #05E05 #Advanced Graph Theory Research #Cellular Automata and Applications #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2405.01166

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the e-positivity of cycle-chord graphs by using the composition method which is developed by Zhou and the author recently. Our method is simpler than the (e)-positivity approach which is used for handling cycle-chords with girth at most 4. We also provide a combinatorial interpretation of the e-coefficients, and conjecture that theta graphs are e-positive.

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