We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree . We prove that, for every > 0, the d...
Martin E. Dyer, Alan M. Frieze, Thomas P. Hayes, E...
Given a positive integer n and a family F of graphs, let R(n, F) denote the maximum number of colors in an edge-coloring of Kn such that no subgraph of Kn belonging to F has disti...
We prove that for every c > 0 there exists a constant K = K(c) such that every graph G with n vertices and minimum degree at least cn contains a cycle of length t for every even...
An acyclic edge colouring of a graph is a proper edge colouring having no 2-coloured cycle, that is, a colouring in which the union of any two colour classes forms a linear forest...
In an edge deletion problem one is asked to delete at most k edges from a given graph such that the resulting graph satisfies a certain property. In this work, we study four NP-co...