The e-positivity of two families of (claw, 2K₂)-free graphs

2019/12/20 by Grace M. X. Li, Li, Grace M. X., Arthur L. B. Yang +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1912.09717

openalex publication_date 2019/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by Stanley's conjecture about the e-positivity of claw-free incomparability graphs, Hamel and her collaborators studied the e-positivity of (claw, H)-free graphs, where H is a four-vertex graph. In this paper we establish the e-positivity of generalized pyramid graphs and 2K₂-free unit interval graphs, which are two important families of (claw, 2K₂)-free graphs. Hence we affirmatively solve one problem proposed by Hamel, Hoàng and Tuero, and another problem considered by Foley, Hoàng and Merkel.

Citations

• Triangular Ladders P_d,2 are e-positive

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