The pair length of a graph G is the maximum positive integer k, such that the vertex set of G can be partitioned into disjoint pairs {x, x }, such that d(x, x ) k for every x V (...
For an oriented graph G with n vertices, let f(G) denote the minimum number of transitive subtournaments that decompose G. We prove several results on f(G). In particular, if G is...
For an integer n 3, a rank-n matroid is called an n-spike if it consists of n three-point lines through a common point such that, for all k {1, 2, . . . , n - 1}, the union of e...
We study the problem of minimal triangulation of graphs. One of the first algorithms to solve this problem was Lex M, which was presented in 1976. A new algorithm, and a simplific...
A computer package is being developed at Bayreuth for the generation and investigation of discrete structures. The package is a C and C++ class library of powerful algorithms endow...
Given a 3-connected biased graph with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of is uniquely represented by .