Packing 3-vertex Paths in Cubic 3-connected Graphs
نویسنده
چکیده
Let v(G) and λ(G) be the number of vertices and the maximum number of disjoint 3-vertex paths in G, respectively. We discuss the following old Problem. Is the following claim true ? (P ) if G is a 3-connected and cubic graph, then λ(G) = bv(G)/3c. We show, in particular, that claim (P ) is equivalent to some seemingly stronger claims (see 3.1). It follows that if claim (P ) is true, then Reed’s dominating graph conjecture is true for cubic 3-connected graphs.
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تاریخ انتشار 2008