In unweighted case, approximation ratio for the independent set problem has been analyzed in terms of the graph parameters, such as the number of vertices, maximum degree, and aver...
Given a graph G = (V, E), a proper vertex colouring of V is t-frugal if no colour appears more than t times in any neighbourhood and is acyclic if each of the bipartite graphs con...
We consider the problem of generating a random q-colouring of a graph G = (V, E). We consider the simple Glauber Dynamics chain. We show that if for all v V the average degree of...
Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; sim...
We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n =...