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 ( 2 a , 0 ) , T M ( 0 , 2 a ) } 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.
Full Text
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call