Injective Colouring for H-Free Graphs
| Autor: | Barnaby Martin, Siani Smith, Nikola Jedličková, Daniël Paulusma, Jan Bok |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Computer Science – Theory and Applications ISBN: 9783030794156 CSR |
| DOI: | 10.1007/978-3-030-79416-3_2 |
| Popis: | A function \(c:V(G)\rightarrow \{1,2,\ldots ,k\}\) is a k-colouring of a graph G if \(c(u)\ne c(v)\) whenever u and v are adjacent. If any two colour classes induce the disjoint union of vertices and edges, then c is called injective. Injective colourings are also known as L(1, 1)-labellings and distance 2-colourings. The corresponding decision problem is denoted Injective Colouring. A graph is H-free if it does not contain H as an induced subgraph. We prove a dichotomy for Injective Colouring for graphs with bounded independence number. Then, by combining known with further new results, we determine the complexity of Injective Colouring on H-free graphs for every H except for one missing case. |
| Databáze: | OpenAIRE |
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