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Your search keyword '"Michitaka Furuya"' showing total 134 results
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134 results on '"Michitaka Furuya"'

1. Forbidden subgraphs for constant domination number

Author

Michitaka Furuya

Subjects
mathematics - combinatorics, Mathematics, QA1-939
Abstract

In this paper, we characterize the sets $\mathcal{H}$ of connected graphs such that there exists a constant $c=c(\mathcal{H})$ satisfying $\gamma (G)\leq c$ for every connected $\mathcal{H}$-free graph $G$, where $\gamma (G)$ is the domination number of $G$.

Published
2018
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2. Path-factors involving paths of order seven and nine

Author

Yoshimi Egawa and Michitaka Furuya

Subjects
path-factor, matching, hypomatchable graph, Mathematics, QA1-939
Abstract

In this paper, we show the following two theorems (here $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$): (i)~If a graph $G$ satisfies $c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{7}\}$-factor. (ii)~If a graph $G$ satisfies $c_{1}(G-X)+c_{3}(G-X)+\frac{2}{3}c_{5}(G-X)+\frac{1}{3}c_{7}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{9}\}$-factor.

Published
2016
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38. Degree Sum Condition for the Existence of Spanning k-Trees in Star-Free Graphs

Author

Shun ichi Maezawa, Ryota Matsubara, Takamasa Yashima, Shoichi Tsuchiya, Haruhide Matsuda, and Michitaka Furuya

Subjects
spanning tree, Spanning tree, Degree (graph theory), Applied Mathematics, degree sum condition, Star (graph theory), Combinatorics, star-free, 05c05, k-tree, QA1-939, Discrete Mathematics and Combinatorics, K-tree, 05c50, Mathematics
Abstract

For an integer k ≥ 2, a k-tree T is defined as a tree with maximum degree at most k. If a k-tree T spans a graph G, then T is called a spanning k-tree of G. Since a spanning 2-tree is a Hamiltonian path, a spanning k-tree is an extended concept of a Hamiltonian path. The first result, implying the existence of k-trees in star-free graphs, was by Caro, Krasikov, and Roditty in 1985, and independently, Jackson and Wormald in 1990, who proved that for any integer k with k ≥ 3, every connected K1,k-free graph contains a spanning k-tree. In this paper, we focus on a sharp condition that guarantees the existence of a spanning k-tree in K1,k+1-free graphs. In particular, we show that every connected K1,k+1-free graph G has a spanning k-tree if the degree sum of any 3k − 3 independent vertices in G is at least |G| − 2, where |G| is the order of G.

Published
2022

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