Degree Sum and Vertex Dominating Paths
نویسندگان
چکیده
A vertex dominating path in a graph is a path P such that every vertex outside P has a neighbor on P . In 1988 H. Broersma stated a result implying that every n-vertex kconnected graph G such that σ(k+2)(G) ≥ n− 2k − 1 contains a dominating path. We show that every n-vertex k-connected graph with σ2(G) ≥ 2n k+2 + f(k) contains a dominating path of length at most O(|T |), where T is a minimum dominating set of vertices. The main result is that every n-vertex k-connected graph such that σ2(G) ≥ 2n k+2 + f(k) contains a path of length at most O(|T |) through any set of T vertices where |T | = o(n).
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