The Merino-Welsh conjecture holds for series-parallel graphs

نویسندگان

  • Steven D. Noble
  • Gordon F. Royle
چکیده

The Merino-Welsh conjecture asserts that the number of spanning trees of a graph is no greater than the maximum of the numbers of totally cyclic orientations and acyclic orientations of that graph. We prove this conjecture for the class of series-parallel graphs.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The graph formulation of the union-closed sets conjecture

In 1979 Frankl conjectured that in a finite non-trivial union-closed collection of sets there has to be an element that belongs to at least half the sets. We show that this is equivalent to the conjecture that in a finite non-trivial graph there are two adjacent vertices each belonging to at most half of the maximal stable sets. In this graph formulation other special cases become natural. The ...

متن کامل

A note on Fouquet-Vanherpe’s question and Fulkerson conjecture

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

متن کامل

A Tutte polynomial inequality for lattice path matroids

Let M be a matroid without loops or coloops and let TM be its Tutte polynomial. In 1999 Merino and Welsh conjectured that max(TM (2, 0), TM (0, 2)) ≥ TM (1, 1) for graphic matroids. Ten years later, Conde and Merino proposed a multiplicative version of the conjecture which implies the original one. In this paper we show the validity of the multiplicative conjecture when M is a lattice path matr...

متن کامل

-λ coloring of graphs and Conjecture Δ ^ 2

For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...

متن کامل

Partial List Colouring of Certain Graphs

The partial list colouring conjecture due to Albertson, Grossman, and Haas [1] states that for every s-choosable graph G and every assignment of lists of size t, 1 6 t 6 s, to the vertices of G there is an induced subgraph of G on at least t|V (G)| s vertices which can be properly coloured from these lists. In this paper, we show that the partial list colouring conjecture holds true for certain...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Eur. J. Comb.

دوره 38  شماره 

صفحات  -

تاریخ انتشار 2014