3 papers
math.CO2024
Induced even cycles in locally sparse graphs
Laihao Ding, Jun Gao, Hong Liu +2
A graph is -sparse if for every pair of vertex subsets with , . In this paper we prove that for every and…
math.CO2022
Balanced subdivisions of cliques in graphs
Bingyu Luan, Yantao Tang, Guanghui Wang +1
Given a graph , a balanced subdivision of is a graph obtained from by subdividing every edge the same number of times. In 1984, Thomassen conjectured that for each integ…
math.CO2021
Crux and long cycles in graphs
John Haslegrave, Jie Hu, Jaehoon Kim +3
We introduce a notion of the \emph{crux} of a graph , measuring the order of a smallest dense subgraph in . This simple-looking notion leads to some generalisations of known…