K. Ozeki

collaborators

4 papers

math.CO2026

A Note on GrÃ¼nbaum's Conjecture about Longest Cycles and Paths

Masaki Kashima, Kenta Ozeki, Leilei Zhang

Let $c (G)$ denote the circumference of a graph $G$ , i.e., the number of vertices in its longest cycle. For positive integers $n$ and $k$ with $n > k$ , let $Γ (n; k)$ be the cla…

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.CO2025

A generalization of an ear decomposition and k-trees in highly connected star-free graphs

Shun-ichi Maezawa, Kenta Ozeki, Masaki Yamamoto +1

In this paper, we introduce a generalized version of an ear decomposition, called a $j$ -spider decomposition, for $j$ -connected star-free graphs with $j \geq 2$ . Its application en…

math.CO2025

Odd coloring of $k$ -trees

Masaki Kashima, Kenta Ozeki

An odd coloring of a graph is a proper coloring such that every non-isolated vertex has a color that appears at an odd number of its neighbors. This notion was introduced by PetrÅ¡…

A Note on GrÃ¼nbaum's Conjecture about Longest Cycles and Paths

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

A generalization of an ear decomposition and k-trees in highly connected star-free graphs

Odd coloring of k-trees

Odd coloring of $k$ -trees