M. Furuya

activity

20242026

collaborators

5 papers

math.CO2026

On the number of 4-contractible edges in plane triangulations

Toshiki Abe, Michitaka Furuya, Raiji Mukae +1

In 2007, Ando and Egawa proved a theorem which provides a lower bound on the number of contractible edges preserving $4$ -connectedness in $4$ -connected graphs. In this paper, we re…

math.CO2025

A new strategy for finding spanning trees without small degree stems

Michitaka Furuya, Shoichi Tsuchiya

For an integer $k \geq 2$ , a spanning tree of a graph without vertices of degree from $2$ to $k$ is called a {\it $[2, k]$ -ST} of the graph. The concept of $[2, k]$ -STs is a natural e…

math.CO2024

Refinements of degree conditions for the existence of a spanning tree without small degree stems

Michitaka Furuya, Akira Saito, Shoichi Tsuchiya

A spanning tree of a graph without no vertices of degree $2$ is called a {\it homeomorphically irreducible spanning tree} (or a {\it HIST}) of the graph. Albertson, Berman, Hutchin…

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.CO2024

Ramsey-type problems on induced covers and induced partitions toward the GyÃ¡rfÃ¡s-Sumner conjecture

Shuya Chiba, Michitaka Furuya

GyÃ¡rfÃ¡s and Sumner independently conjectured that for every tree $T$ , there exists a function $f_{T} : N \to N$ such that every $T$ -free graph $G$ satisfie…