Kenta Noguchi

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20232026

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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…

Spanning plane subgraphs of 1-plane graphs

HIST-Critical Graphs and Malkevitch's Conjecture

Spanning plane subgraphs of $1$ -plane graphs