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- W2142635515 abstract "Let k ≥ 2 , l ≥ 2 , m ≥ 0 and n ≥ 1 be integers, and let G be a connected graph. If there exists a subgraph H of G such that for every vertex v of G , the distance between v and H is at most m , then we say that H m -dominates G . A tree whose maximum degree is at most k is called a k -tree. Define α l ( G ) = max { | S | : S ⊆ V ( G ) , d G ( x , y ) ≥ l for all distinct x , y ∈ S } , where d G ( x , y ) denotes the distance between x and y in G . We prove the following theorem and show that the condition is sharp. If an n -connected graph G satisfies α 2 ( m + 1 ) ( G ) ≤ ( k − 1 ) n + 1 , then G has a k -tree that m -dominates G . This theorem is a generalization of both a theorem of Neumann-Lara and Rivera-Campo on a spanning k -tree in an n -connected graph and a theorem of Broersma on an m -dominating path in an n -connected graph." @default.
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- W2142635515 date "2016-02-01" @default.
- W2142635515 modified "2023-10-18" @default.
- W2142635515 title "m-dominating k-trees of graphs" @default.
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- W2142635515 doi "https://doi.org/10.1016/j.disc.2015.10.013" @default.
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