Y. Egawa

activity

20152025

most citedThe existence of a path-factor without small odd paths

3 citations · 3 across the 4 of their papers we have counts for

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5 papers · 1 filter

math.CO2025

Spanning path-cycle systems with given end-vertices in regular graphs (full version)

Yoshimi Egawa, Mikio Kano, Kenta Ozeki

We prove the following theorem. Let $r \geq 4$ be an integer, and $G$ be a $K_{1, r}$ -free $r$ -edge-connected $r$ -regular graph. Then, for every set $W$ of even number of vertices of…

math.CO2024

Forbidden subgraphs generating a finite set of graphs with minimum degree three and large girth

Yoshimi Egawa, Michitaka Furuya

For a family $H$ of graphs, a graph $G$ is said to be {\it $H$ -free} if $G$ contains no member of $H$ as an induced subgraph. We let $\tilde{\mathcal{…

math.CO2017

Sufficient conditions for the existence of a path-factor which are related to odd components

Yoshimi Egawa, Michitaka Furuya, Kenta Ozeki

In this paper, we are concerned with sufficient conditions for the existence of a ${P_{2}, P_{2 k + 1}}$ -factor. We prove that for $k \geq 3$ , there exists $ε_{k} > 0$ such th…

math.CO2015

Path-factors involving paths of order seven and nine

Yoshimi Egawa, Michitaka Furuya

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}…

math.CO2015★ 3 cited

The existence of a path-factor without small odd paths

Yoshimi Egawa, Michitaka Furuya

In this paper, we show that if a graph $G$ satisfies $c_{1} (G - X) + \frac{2}{3} c_{3} (G - X) \leq \frac{4}{3} ∣ X ∣ + \frac{1}{3}$ for all $X \subseteq V (G)$ , then $G$ has a ${P_{2}, P_{5}}$ -f…