Xinmin Hou

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math.CO2025

Unavoidable induced subgraphs forced by graphs with many vertices of prescribed properties

Jin Sun, Xinmin Hou

Given a function $p : V (G) \to N$ and an integer $k \geq 0$ , define $p_{k} (G)$ as the number of vertices with $p (v) \geq k$ . We say that $p_{k} (G)$ is bounded for all $\HH$-free gra…

math.CO2025

Induced subgraphs of graphs with large deficiency

Jin Sun, Xinmin Hou

The deficiency of a graph $G$ , denoted by $\kd(G)$, is the number of vertices not saturated by a maximum matching. A bone $B_{i}$ is the tree obtained by attaching two pendent edges…

math.CO2024

A Ramsey-type theorem on deficiency

Jin Sun, Xinmin Hou

Ramsey's Theorem states that a graph $G$ has bounded order if and only if $G$ contains no complete graph $K_{n}$ or empty graph $E_{n}$ as its induced subgraph. The Gyárfás-Sumner conj…

math.CO2023

Ramsey-type results on parameters related to domination

Jin Sun, Xinmin Hou

The following inequality chain $i r (G) \leq γ (G) \leq i (G) \leq α (G) \leq Γ (G) \leq I R (G)$ is known as a domination chain, where $i r (G), γ (G), i (G), α (G), Γ (G)$ , and $I R (G)$ are the…