Some inequalities for the Tutte polynomial

2010/04/15 by L. E. Chavez-Lomelí, Laura E. Chávez-Lomelí, C. Merino +9
Computer Science · Mathematics · #05C31 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #math.CO #msc:05C31

paper · pdf · doi:10.48550/arxiv.1004.2639

17 pages

arxiv created 2010/04/15 · openalex publication_date 2010/04/15 · arxiv updated 2010/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portions of the line segments x+y=p lying in the positive quadrant. Every coloopless paving matroids is in the class of matroids which contain two disjoint bases or whose ground set is the union of two bases of M*. For this latter class we give a proof that T_M(a,a) <= max T_M(2a,0), T_M(0,2a) for a >= 2. We conjecture that T_M(1,1) <= max T_M(2,0), T_M(0,2) for the same class of matroids. We also prove this conjecture for some families of graphs and matroids.

Citations

• Acyclic orientations of graphs
• On the structure of the h-vector of a paving matroid

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