Degree sum conditions for oriented forests in digraphs |
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Authors: | Shengning Qiao |
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Institution: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China |
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Abstract: | Let F be an oriented forest with n vertices and m arcs and D be a digraph without loops and multiple arcs. In this note we prove that D contains a subdigraph isomorphic to F if D has at least n vertices and min{d+(u)+d+(v),d−(u)+d−(v),d+(u)+d−(v)}≥2m−1 for every pair of vertices u,v∈V(D) with uv∉A(D). This is a common generalization of two results of Babu and Diwan, one on the existence of forests in graphs under a degree sum condition and the other on the existence of oriented forests in digraphs under a minimum degree condition. |
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Keywords: | Oriented forests Subdigraphs Degree sum conditions |
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