Abstract. Markov random fields are often used to model high dimensional distributions in a number of applied areas. A number of recent papers have studied the problem of reconstruc...
A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring...
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge ...
We characterize the edge-signed graphs in which every 'significant' positive closed walk (or combination of walks) has even length, under seven different criteria for si...
The problem of computing the chromatic number of a P5-free graph (a graph which contains no path on 5 vertices as an induced subgraph) is known to be NP-hard. However, we show tha...