Bok, J. and Jedličková, N. and Martin, B. and Paulusma, D. and Smith, S. (2021) 'Injective colouring for H-free graphs.', CSR 2021 Sochi, 28 Jun - 02 Jul 2021.
Abstract
A function c : V (G) → {1, 2, . . . , k} is a k-colouring of a graph G if c(u) 6= 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.
| Item Type: | Conference item (Paper) |
|---|---|
| Full text: | Publisher-imposed embargo (AM) Accepted Manuscript Available under License - Creative Commons Attribution. File format - PDF (470Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://logic.pdmi.ras.ru/~csr/ |
| Date accepted: | 08 February 2021 |
| Date deposited: | 16 April 2021 |
| Date of first online publication: | 2021 |
| Date first made open access: | No date available |
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