We call a matrix A nearly totally unimodular if it can be obtained from a totally unimodular matrix à by adding to each row of à an integer multiple of some fixed row a of Ã. For an integer vector b and a nearly totally unimodular matrix A, we denote by PA,b the integer hull of the set {x ∈ R | Ax ≤ b}. We show that PA,b has the integer decomposition property and that we can find a decompositio...

‎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...

We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.

In this paper, we give the correlation and difference between M-convex fuzzy process and SLW-convex fuzzy process, and present some basic properties of these convex fuzzy processes, which improve some known results about the connection between those convex fuzzy processes and their graphs. In addition, we introduce a new notion of s-convex fuzzy process as a generalization of M-convex fuzzy pro...

A graph G is pluperfect if one can add new multiple edges to obtain a multi graph M satisfying: (1) G spans M, (2) the degrees of the nodes of M are consecutive integers, (3) G and M have the same minimum degree. Our purpose is to display several families of pluperfect graphs in order to L Introduction My good friends Mehdi Behzad and Gary Chartrand wrote a note [1] titled "No graph is perfect"...