Dyck's map (3, 7) 8 is a counterexample to a clique covering conjecture
A Vince, S Wilson�- Journal of Combinatorial Theory, Series B, 1992 - Elsevier
A Vince, S Wilson
Journal of Combinatorial Theory, Series B, 1992•Elsevier… Dyck [3] in 1880 in connection with Riemann surfaces and led to a good deal of interest
in maps in general. The underlying graph Go of { 3, 7) 8 provides a counterexample to the
conjecture above. This particular graph seemed a likely candidate as a counterexample for
the following reasons. Because of its symmetry, inequality (1) need only be checked for a
single edge. The …
in maps in general. The underlying graph Go of { 3, 7) 8 provides a counterexample to the
conjecture above. This particular graph seemed a likely candidate as a counterexample for
the following reasons. Because of its symmetry, inequality (1) need only be checked for a
single edge. The …
Abstract
Let c(G) denote the minimum number of cliques necessary to cover all edges of a graph G. A counterexample is provided to a conjecture communicated by P. Erdős. If c(G − e) < c(G) for every edge e, then G contains no triangles.
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