Spanning Trees with Few Peripheral Branch Vertices
نویسندگان
چکیده
منابع مشابه
Spanning trees with few branch vertices
A branch vertex in a tree is a vertex of degree at least three. We prove that, for all s ≥ 1, every connected graph on n vertices with minimum degree at least ( 1 s+3 + o(1))n contains a spanning tree having at most s branch vertices. Asymptotically, this is best possible and solves a problem of Flandrin, Kaiser, Kuz̆el, Li and Ryjác̆ek, which was originally motivated by an optimization problem i...
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Let G be a connected claw-free graph. A conjecture of Matsuda, Ozeki, and Yamashita [9] posits the existence of either a spanning tree with few branch vertices or a large independent set of small degree sum. The possible appearances of this minimal spanning tree may be ruled out piecemeal. This paper treats one particular class, which may be the easiest to rule out but also fits, to our knowled...
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The problem of finding a spanning tree with few leaves is motivated by the design of communication networks, where the cost of the devices depends on their routing functionality (ending, forwarding, or routing a connection). Besides this application, the problem has its own theoretical importance as a generalization of the Hamiltonian path problem. Lu and Ravi showed that there is no constant f...
متن کاملSpanning Trees with a Bounded Number of Branch Vertices in a Claw-Free Graph
Let k be a non-negative integer. A branch vertex of a tree is a vertex of degree at least three. We show two sufficient conditions for a connected clawfree graph to have a spanning tree with a bounded number of branch vertices: (i) A connected claw-free graph has a spanning tree with at most k branch vertices if its independence number is at most 2k + 2. (ii) A connected clawfree graph of order...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2021
ISSN: 1027-5487
DOI: 10.11650/tjm/201201