Some inequalities for the Tutte polynomial

  • Authors:

  • Laura E. Chávez-Lomelí;Criel Merino;Steven D. Noble;Marcelino Ramírez-Ibáñez

  • Affiliations:

  • Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Avenida San Pablo 180, colonia Reynosa Tamaulipas, Delegación Azcapotzalco, Mexico;Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Científica, Circuito Exterior, C.U. Coyoacán 04510, México D.F., Mexi ...;Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, UK;Instituto de Matemáticas, Universidad Nacional Autónoma de México, Area de la Investigación Científica, Circuito Exterior, C.U. Coyoacán 04510, México D.F., Mexi ...

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2011

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Abstract

We prove that the Tutte polynomial of a coloopless paving matroid is convex along the portion of the line x+y=p lying in the positive quadrant. Every coloopless paving matroid is in the class of matroids which contain two disjoint bases or whose ground set is the union of two bases. 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.