A Ramsey-type theorem on deficiency
| Autor: | Sun, Jin, Hou, Xinmin |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 Gy\'arf\'as-Sumner conjecture says that a graph $G$ has bounded chromatic number if and only if it contains no induced subgraph isomorphic to $K_n$ or a tree $T$. The deficiency of a graph is the number of vertices that cannot be covered by a maximum matching. In this paper, we prove a Ramsey type theorem for deficiency, i.e., we characterize all the forbidden induced subgraphs for graphs $G$ with bounded deficiency. As an application, we answer a question proposed by Fujita, Kawarabayashi, Lucchesi, Ota, Plummer and Saito (JCTB, 2006). Comment: 17 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|