The Incidence Chromatic Number of Toroidal Grids
An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f, or the edge vw equals e or f. The incidence chromatic number of G is the smallest k for which there exists a mapping from the set...
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2013-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1663 |
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doaj-9c581d587513410bba3bbf53c247b9712021-09-05T17:20:19ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922013-05-0133231532710.7151/dmgt.1663The Incidence Chromatic Number of Toroidal GridsSopena Éric0Wu Jiaojiao1Univ. Bordeaux, LaBRI, UMR5800, F-33400 Talence CNRS, LaBRI, UMR5800, F-33400 TalenceDepartment of Applied Mathematics National Sun Yat-sen University, TaiwanAn incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f, or the edge vw equals e or f. The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences. In this paper, we prove that the incidence chromatic number of the toroidal grid Tm,n = Cm2Cn equals 5 when m, n ≡ 0(mod 5) and 6 otherwise.https://doi.org/10.7151/dmgt.1663incidence coloringcartesian product of cyclestoroidal grid |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Sopena Éric Wu Jiaojiao |
| spellingShingle |
Sopena Éric Wu Jiaojiao The Incidence Chromatic Number of Toroidal Grids Discussiones Mathematicae Graph Theory incidence coloring cartesian product of cycles toroidal grid |
| author_facet |
Sopena Éric Wu Jiaojiao |
| author_sort |
Sopena Éric |
| title |
The Incidence Chromatic Number of Toroidal Grids |
| title_short |
The Incidence Chromatic Number of Toroidal Grids |
| title_full |
The Incidence Chromatic Number of Toroidal Grids |
| title_fullStr |
The Incidence Chromatic Number of Toroidal Grids |
| title_full_unstemmed |
The Incidence Chromatic Number of Toroidal Grids |
| title_sort |
incidence chromatic number of toroidal grids |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae Graph Theory |
| issn |
2083-5892 |
| publishDate |
2013-05-01 |
| description |
An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f, or the edge vw equals e or f. The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences. In this paper, we prove that the incidence chromatic number of the toroidal grid Tm,n = Cm2Cn equals 5 when m, n ≡ 0(mod 5) and 6 otherwise. |
| topic |
incidence coloring cartesian product of cycles toroidal grid |
| url |
https://doi.org/10.7151/dmgt.1663 |
| work_keys_str_mv |
AT sopenaeric theincidencechromaticnumberoftoroidalgrids AT wujiaojiao theincidencechromaticnumberoftoroidalgrids AT sopenaeric incidencechromaticnumberoftoroidalgrids AT wujiaojiao incidencechromaticnumberoftoroidalgrids |
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