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November 2006 Disjoint stars and forbidden subgraphs
Shinya Fujita
Hiroshima Math. J. 36(3): 397-403 (November 2006). DOI: 10.32917/hmj/1171377081

Abstract

Let $r,k$ be integers with $r\ge 3, k\ge 2$. We prove that if $G$ is a $K_{1,r}$-free graph of order at least $(k-1)(2r-1)+1$ with $\delta(G)\ge 2$, then $G$ contains $k$ vertex-disjoint copies of $K_{1,2}$. This result is motivated by the problem of characterizing a forbidden subgraph $H$ which satisfies the statement "every $H$-free graph of sufficiently large order with minimum degree at least $t$ contains $k$ vertex-disjoint copies of a star $K_{1,t}$." In this paper, we also give the answer to this problem.

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Shinya Fujita. "Disjoint stars and forbidden subgraphs." Hiroshima Math. J. 36 (3) 397 - 403, November 2006. https://doi.org/10.32917/hmj/1171377081

Information

Published: November 2006
First available in Project Euclid: 13 February 2007

zbMATH: 1123.05074
MathSciNet: MR2290665
Digital Object Identifier: 10.32917/hmj/1171377081

Subjects:
Primary: 05C70, 05C75

Rights: Copyright © 2006 Hiroshima University, Mathematics Program

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Vol.36 • No. 3 • November 2006
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