The matroidal version of the Merino–Welsh conjecture states that the Tutte polynomial TM (x,
y) of any matroid M without loops and coloops satisfies that max⁡(TM (2, 0), TM (0, 2))⩾ TM …

We give two proofs that the h-vector of any paving matroid is a pure O-sequence, thus
answering in the affirmative a conjecture made by Stanley, for this particular class of …

Abstract In 1999, Merino and Welsh conjectured that evaluations of the Tutte polynomial of a
graph satisfy an inequality. In this short article, we show that the conjecture generalized to …

Let M be a matroid without loops or coloops and let T (M; x, y) be its Tutte polynomial. In
1999 Merino and Welsh conjectured that max⁡(T (M; 2, 0), T (M; 0, 2))≥ T (M; 1, 1) holds for …

The Merino–Welsh conjecture holds for series–parallel graphs - ScienceDirect Skip to main
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The Merino-Welsh conjectures say that subject to conditions, there is an inequality among
the Tutte-polynomial evaluations $ T (M; 2, 0) $, $ T (M; 0, 2) $, and $ T (M; 1, 1) $. We …

Abstract (EN) Graph polynomials are polynomials associated to graphs that encode the
number of subgraphs with given properties. We list different frameworks used to define …

We calculate exponential growth constants describing the asymptotic behavior of several
quantities enumerating classes of orientations of arrow variables on the bonds of several …

We infer upper and lower bounds on the exponential growth constants α (Λ) α (Λ), α _0 (Λ) α
0 (Λ), and β (Λ) β (Λ) describing the large-n behavior of, respectively, the number of acyclic …

In this paper, we deal with counting and enumerating problems for two types of graph
orientations: acyclic and totally cyclic orientations. Counting is known to be# P-hard for both …