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We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm,...
Let ;k g be the class of k-connected cubic graphs of girth at least g. For several choices of k and g, we determine a set Ok g of graph operations, for which, if G and H are graph...
Given a graph G = (V, E) and a positive integer k, the PARTITION INTO CLIQUES (PIC) decision problem consists of deciding whether there exists a partition of V into k disjoint sub...
We show that the firefighter problem is NP-complete for cubic graphs. We also show that given a rooted tree of maximum degree three in which every leaf is the same distance from t...
We consider cubic graphs formed with k 2 disjoint claws Ci K1,3 (0 i k-1) such that for every integer i modulo k the three vertices of degree 1 of Ci are joined to the three v...
Jean-Luc Fouquet, Henri Thuillier, Jean-Marie Vanh...
We consider the performance of a simple greedy matching algorithm MINGREEDY when applied to random cubic graphs. We show that if λn is the expected number of vertices not matched...
For a connected graph G, let L(G) denote the maximum number of leaves in a spanning tree in G. The problem of computing L(G) is known to be NP-hard even for cubic graphs. We improv...