Kenta Noguchi

activity

20232026

collaborators

6 papers

math.CO2026

Note on the thickness of the Cartesian product of a complete graph and a path

Kenta Noguchi

We determine the thickness of the Cartesian product $K_{6 p + 4} □ P_{2}$ for $p \geq 0$ and of the Cartesian product $K_{8} □ P_{m}$ for $m \geq 1$ , where $K_{n}$ and $P_{m}$ denote…

math.CO2025

Toroidal Cartesian Products Where One Factor is 3-Connected

Elizabeth Badgett, Christian Millichap, Kenta Noguchi

In this paper, we show that if $G$ is $3$ -connected, then the Cartesian product of graphs $G □ H$ embeds on the torus if and only if $G$ is outer-cylindrical and $H$ is a pat…

math.CO2024

Spanning plane subgraphs of $1$ -plane graphs

Kenta Noguchi, Katsuhiro Ota, Yusuke Suzuki

A graph drawn on the plane is called $1$ -plane if each edge is crossed at most once by another edge. In this paper, we show that every $4$ -connected $1$ -plane graph has a connected…

math.CO2024

HIST-Critical Graphs and Malkevitch's Conjecture

Jan Goedgebeur, Kenta Noguchi, Jarne Renders +1

In a given graph, a HIST is a spanning tree without $2$ -valent vertices. Motivated by developing a better understanding of HIST-free graphs, i.e. graphs containing no HIST, in this…

math.CO2023

Spanning trees for many different numbers of leaves

Kenta Noguchi, Carol T. Zamfirescu

Let $G$ be a connected graph and $L (G)$ the set of all integers $k$ such that $G$ contains a spanning tree with exactly $k$ leaves. We show that for a connected graph $G$ , the set…

math.CO2023

Face sizes and the connectivity of the dual

Gunnar Brinkmann, Kenta Noguchi, Heidi Van den Camp

For each $c \geq 1$ we prove tight lower bounds on face sizes that must be present to allow $1$ - or $2$ -cuts in simple duals of $c$ -connected maps. Using these bounds, we determine t…