Equitable Colorings Of Corona Multiproducts Of Graphs
A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by 𝜒=(G). It is kn...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2017-11-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1992 |
| _version_ | 1827880350152392704 |
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| author | Furmánczyk Hanna Kubale Marek Mkrtchyan Vahan V. |
| author_facet | Furmánczyk Hanna Kubale Marek Mkrtchyan Vahan V. |
| author_sort | Furmánczyk Hanna |
| collection | DOAJ |
| description | A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by 𝜒=(G). It is known that the problem of computation of 𝜒=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013) 103–120]. |
| first_indexed | 2024-03-12T18:20:22Z |
| format | Article |
| id | doaj.art-a6fe15ed05d445bca32d797b8b2b653c |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T18:20:22Z |
| publishDate | 2017-11-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-a6fe15ed05d445bca32d797b8b2b653c2023-08-02T08:59:08ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922017-11-013741079109410.7151/dmgt.1992dmgt.1992Equitable Colorings Of Corona Multiproducts Of GraphsFurmánczyk Hanna0Kubale Marek1Mkrtchyan Vahan V.2Institute of Informatics, University of Gdánsk Wita Stwosza 57, 80-952 Gdánsk, PolandDepartment of Algorithms and System Modelling Gdánsk University of Technology Narutowicza 11/12, 80-233 Gdánsk, PolandDepartment of Informatics and Applied Mathematics Yerevan State University, Yerevan, ArmeniaA graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by 𝜒=(G). It is known that the problem of computation of 𝜒=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013) 103–120].https://doi.org/10.7151/dmgt.1992corona graphequitable chromatic numberequitable coloring conjectureequitable graph coloringmultiproduct of graphsnp-completenesspolynomial algorithm. |
| spellingShingle | Furmánczyk Hanna Kubale Marek Mkrtchyan Vahan V. Equitable Colorings Of Corona Multiproducts Of Graphs Discussiones Mathematicae Graph Theory corona graph equitable chromatic number equitable coloring conjecture equitable graph coloring multiproduct of graphs np-completeness polynomial algorithm. |
| title | Equitable Colorings Of Corona Multiproducts Of Graphs |
| title_full | Equitable Colorings Of Corona Multiproducts Of Graphs |
| title_fullStr | Equitable Colorings Of Corona Multiproducts Of Graphs |
| title_full_unstemmed | Equitable Colorings Of Corona Multiproducts Of Graphs |
| title_short | Equitable Colorings Of Corona Multiproducts Of Graphs |
| title_sort | equitable colorings of corona multiproducts of graphs |
| topic | corona graph equitable chromatic number equitable coloring conjecture equitable graph coloring multiproduct of graphs np-completeness polynomial algorithm. |
| url | https://doi.org/10.7151/dmgt.1992 |
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