Injective Colouring for H-Free Graphs

Jan Bok; Nikola Jedličková; Barnaby Martin; Daniël Paulusma; Siani Smith

doi:10.1007/978-3-030-79416-3_2

Injective Colouring for H-Free Graphs

Jan Bok, Nikola Jedličková, Barnaby Martin, Daniël Paulusma, Siani Smith^*

^*Corresponding author for this work

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

2 Citations (Scopus)

Abstract

A function c: V(G) → { 1, 2, …, k} is a k-colouring of a graph G if c(u) ≠ 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.

Original language	English
Title of host publication	Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings
Editors	Rahul Santhanam, Daniil Musatov
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	18-30
Number of pages	13
ISBN (Electronic)	9783030794163
ISBN (Print)	9783030794156
DOIs	https://doi.org/10.1007/978-3-030-79416-3_2
Publication status	Published - 17 Jun 2021
Event	16th International Computer Science Symposium in Russia, CSR 2021 - Sochi, Russian Federation Duration: 28 Jun 2021 → 2 Jul 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12730 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Computer Science Symposium in Russia, CSR 2021
Country/Territory	Russian Federation
City	Sochi
Period	28/06/21 → 2/07/21

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

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Bok, J., Jedličková, N., Martin, B., Paulusma, D., & Smith, S. (2021). Injective Colouring for H-Free Graphs. In R. Santhanam, & D. Musatov (Eds.), Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings (pp. 18-30). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12730 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-79416-3_2

Bok, Jan ; Jedličková, Nikola ; Martin, Barnaby et al. / Injective Colouring for H-Free Graphs. Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings. editor / Rahul Santhanam ; Daniil Musatov. Springer Science and Business Media Deutschland GmbH, 2021. pp. 18-30 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "A function c: V(G) → { 1, 2, …, k} is a k-colouring of a graph G if c(u) ≠ 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.",

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Bok, J, Jedličková, N, Martin, B, Paulusma, D & Smith, S 2021, Injective Colouring for H-Free Graphs. in R Santhanam & D Musatov (eds), Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12730 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 18-30, 16th International Computer Science Symposium in Russia, CSR 2021, Sochi, Russian Federation, 28/06/21. https://doi.org/10.1007/978-3-030-79416-3_2

Injective Colouring for H-Free Graphs. / Bok, Jan; Jedličková, Nikola; Martin, Barnaby et al.
Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings. ed. / Rahul Santhanam; Daniil Musatov. Springer Science and Business Media Deutschland GmbH, 2021. p. 18-30 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12730 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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T1 - Injective Colouring for H-Free Graphs

AU - Bok, Jan

AU - Jedličková, Nikola

AU - Martin, Barnaby

AU - Paulusma, Daniël

AU - Smith, Siani

PY - 2021/6/17

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N2 - A function c: V(G) → { 1, 2, …, k} is a k-colouring of a graph G if c(u) ≠ 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.

AB - A function c: V(G) → { 1, 2, …, k} is a k-colouring of a graph G if c(u) ≠ 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.

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Bok J, Jedličková N, Martin B, Paulusma D, Smith S. Injective Colouring for H-Free Graphs. In Santhanam R, Musatov D, editors, Computer Science – Theory and Applications - 16th International Computer Science Symposium in Russia, CSR 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 18-30. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-79416-3_2

Injective Colouring for H-Free Graphs

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