On covering vertices of a graph by trees |
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Authors: | P. Horak |
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Affiliation: | a University of Washington, Tacoma, WA, USA b Sultan Qaboos University, Oman |
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Abstract: | The purpose of this paper is to initiate study of the following problem: Let G be a graph, and k?1. Determine the minimum number s of trees T1,…,Ts, Δ(Ti)?k,i=1,…,s, covering all vertices of G. We conjecture: Let G be a connected graph, and k?2. Then the vertices of G can be covered by edge-disjoint trees of maximum degree ?k. As a support for the conjecture we prove the statement for some values of δ and k. |
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Keywords: | Covering vertices Path Tree |
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