Yiao Ju

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20212026

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5 papers · 1 filter

math.CO2026

Erdős-Hajnal conjecture beyond five-vertex graphs

Shenwei Huang, Yiao Ju, Yidong Zhou

In 1989, Erdős and Hajnal conjectured that for any graph $H$ , there is a constant $c = c (H) > 0$ such that every $n$ -vertex graph $G$ with no induced copies of $H$ contains a clique or…

math.CO2025

There are finitely many $5$ -vertex-critical $(P_{6}, bull)$ -free graphs

Yiao Ju, Jorik Jooken, Jan Goedgebeur +1

In this paper, we are interested in $4$ -colouring algorithms for graphs that do not contain an induced path on $6$ vertices nor an induced bull, i.e., the graph with vertex set $\{…

math.CO2023

Near Optimal Colourability on Hereditary Graph Families

Yiao Ju, Shenwei Huang

In this paper, we initiate a systematic study on a new notion called near optimal colourability which is closely related to perfect graphs and the Lov{á}sz theta function. A graph…

math.CO2022

Coloring ( $P_{5}$ , kite)-free graphs

Shenwei Huang, Yiao Ju, T. Karthick

Let $P_{n}$ and $K_{n}$ denote the induced path and complete graph on $n$ vertices, respectively. The {\em kite} is the graph obtained from a $P_{4}$ by adding a vertex and making it adj…

math.CO2021

Colouring graphs with no induced six-vertex path or diamond

Jan Goedgebeur, Shenwei Huang, Yiao Ju +1

The diamond is the graph obtained by removing an edge from the complete graph on 4 vertices. A graph is ( $P_{6}$ , diamond)-free if it contains no induced subgraph isomorphic to a six…