Geodesic
On the Star Chromatic Index of Generalized Petersen Graphs
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 427-439 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

The star k-edge-coloring of graph G is a proper edge coloring using k colors such that no path or cycle of length four is bichromatic. The minimum number k for which G admits a star k-edge-coloring is called the star chromatic index of G, denoted by χ_s^′(G). Let GCD(n, k) be the greatest common divisor of n and k. In this paper, we give a necessary and sufficient condition of χ_s^′(P(n, k)) = 4 for a generalized Petersen graph P(n, k) and show that “almost all” generalized Petersen graphs have a star 5-edge-colorings. Furthermore, for any two integers k and n(≥2k + 1) such that GCD(n, k) ≥ 3, P (n, k) has a star 5-edge-coloring, with the exception of the case that GCD(n, k) = 3, k ≠ GCD(n, k) and n/3≡1(mod3).
Keywords: star edge-coloring, star chromatic index, generalized Petersen graph 
@article{DMGT_2021_41_2_a5,
     author = {Zhu, Enqiang and Shao, Zehui},
     title = {On the {Star} {Chromatic} {Index} of {Generalized} {Petersen} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {427--439},
     year = {2021},
     volume = {41},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a5/}
}
TY  - JOUR
AU  - Zhu, Enqiang
AU  - Shao, Zehui
TI  - On the Star Chromatic Index of Generalized Petersen Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2021
SP  - 427
EP  - 439
VL  - 41
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a5/
LA  - en
ID  - DMGT_2021_41_2_a5
ER  - 
%0 Journal Article
%A Zhu, Enqiang
%A Shao, Zehui
%T On the Star Chromatic Index of Generalized Petersen Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2021
%P 427-439
%V 41
%N 2
%U http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a5/
%G en
%F DMGT_2021_41_2_a5
Zhu, Enqiang; Shao, Zehui. On the Star Chromatic Index of Generalized Petersen Graphs. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 427-439. http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a5/

[1] M.O. Albertson, G.G. Chappell, H.A. Kierstead, A. Kündgen and R. Ramamurthi, Coloring with no 2-colored P 4 ’s, Electron. J. Combin. 11 (2004) #R26.

[2] L. Bezegová, B. Lužar, M. Mockovčiaková, R. Soták and R.Škrekovski, Star edge coloring of some classes of grpahs, J. Graph Theory 81 (2016) 73–82. doi:10.1002/jgt.21862

[3] J.A. Bondy and U.S.R. Murty, Graph Theory (Springer, New York, 2008).

[4] Y. Bu, D.W. Cranston, M. Montassier, A. Raspaud and W. Wang, Star-coloring of sparse graphs, J. Graph Theory 62 (2009) 201–209. doi:10.1002/jgt.20392

[5] M. Chen, A. Raspaud and W. Wang, 6-star-coloring of subcubic graphs, J. Graph Theory 72 (2013) 128–145. doi:10.1002/jgt.21636

[6] Z. Dvořák, B. Mohar and R. Šámal, Star chromatic index, J. Graph Theory 72 (2013) 313–326. doi:10.1002/jgt.21644

[7] H.A. Kierstead, A. Kündgen and C. Timmons, Star coloring bipartite planar graphs, J. Graph Theory 60 (2009) 1–10. doi:10.1002/jgt.20342

[8] X.S. Liu and K. Deng, An upper bound on the star chromatic index of graphs with Δ≥7, J. Lanzhou Univ. Nat. Sci. 44 (2008) 94–95.

[9] M.E. Watkins, A theorem on tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory 6 (1969) 152–164. doi:10.1016/S0021-9800(69)80116-X