Geodesic
Interval Incidence Coloring of Subcubic Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 2, pp. 427-441.

Voir la notice de l'article provenant de la source Library of Science

In this paper we study the problem of interval incidence coloring of subcubic graphs. In [14] the authors proved that the interval incidence 4-coloring problem is polynomially solvable and the interval incidence 5-coloring problem is NP-complete, and they asked if Xii(G) ≤ 2Δ(G) holds for an arbitrary graph G. In this paper, we prove that an interval incidence 6-coloring always exists for any subcubic graph G with Δ(G) = 3.
Keywords: interval incidence coloring, incidence coloring, subcubic graph 
@article{DMGT_2017_37_2_a8,
     author = {Ma{\l}afiejska, Anna and Ma{\l}afiejski, Micha{\l}},
     title = {Interval {Incidence} {Coloring} of {Subcubic} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {427--441},
     publisher = {mathdoc},
     volume = {37},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_2_a8/}
}
TY  - JOUR
AU  - Małafiejska, Anna
AU  - Małafiejski, Michał
TI  - Interval Incidence Coloring of Subcubic Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 427
EP  - 441
VL  - 37
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_2_a8/
LA  - en
ID  - DMGT_2017_37_2_a8
ER  - 
%0 Journal Article
%A Małafiejska, Anna
%A Małafiejski, Michał
%T Interval Incidence Coloring of Subcubic Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 427-441
%V 37
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_2_a8/
%G en
%F DMGT_2017_37_2_a8
Małafiejska, Anna; Małafiejski, Michał. Interval Incidence Coloring of Subcubic Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 2, pp. 427-441. http://geodesic.mathdoc.fr/item/DMGT_2017_37_2_a8/

[1] N. Alon, C. McDiarmid and B. Reed, Star arboricity, Combinatorica 12 (1992) 375-380. doi: 10.1007/BF01305230

[2] A. Asratian and R. Kamalian, Investigation on interval edge-colorings of graphs, J. Combin. Theory Ser. B 62 (1994) 34-43. doi: 10.1006/jctb.1994.1053

[3] R.A. Brualdi and J.Q. Massey, Incidence and strong edge colorings of graphs, Discrete Math. 122 (1993) 51-58. doi: 10.1016/0012-365X(93)90286-3

[4] M. Hosseini Dolama, E. Sopena and X. Zhu, Incidence coloring of k-degenerated graphs, Discrete Math. 283 (2004) 121-128. doi: 10.1016/j.disc.2004.01.015

[5] M. Hosseini Dolama and E. Sopena, On the maximum average degree and the inci- dence chromatic number of a graph, Discrete Math. Theor. Comput. Sci. 7 (2005) 203-216.

[6] K. Giaro, Interval edge-coloring, in: Graph Colorings, Contemporary Mathematics AMS, M. Kubale Ed. (2004) 105-121. doi: 10.1090/conm/352/08

[7] K. Giaro, M. Kubale and M. Małafiejski, Compact scheduling in open shop with zero-one time operations, INFOR Inf. Syst. Oper. Res. 37 (1999) 37-47. doi: 10.1080/03155986.1999.11732367

[8] K. Giaro, M. Kubale and M. Małafiejski, Consecutive colorings of the edges of gen- eral graphs, Discrete Math. 236 (2001) 131-143. doi: 0.1016/S0012-365X(00)00437-4

[9] B. Guiduli, On incidence coloring and star arboricity of graphs, Discrete Math. 163 (1997) 275-278. doi: 10.1016/0012-365X(95)00342-T

[10] P. Hall, On representatives of subsets, J. London Math. Soc. 10 (1935) 26-30.

[11] R. Janczewski, A. Małafiejska and M. Małafiejski, Interval incidence coloring of graphs, Zesz. Nauk. Pol. Gd. 13 (2007) 481-488, in Polish.

[12] R. Janczewski, A. Małafiejska and M. Małafiejski, Interval wavelength assignment in all-optical star networks, in: PPAM 2009 (Springer Verlag, 2010) Lecture Notes in Comput. Sci. 6067 (2010) 11-20. doi: 10.1007/978-3-642-14390-8_2

[13] R. Janczewski, A. Małafiejska and M. Małafiejski, Interval incidence coloring of bipartite graphs, Discrete Math. 166 (2014) 131-140. doi: 10.1016/j.dam.2013.10.007

[14] R. Janczewski, A. Małafiejska and M. Małafiejski, Interval incidence graph coloring, Discrete Math. 182 (2015) 73-83. doi: 10.1016/j.dam.2014.03.006

[15] R. Janczewski, A. Małafiejska and M. Małafiejski, On incidence coloring of complete multipartite and semicubic bipartite graphs, Discuss. Math. Graph Theory (2017), in press.

[16] X. Li and J. Tu, NP-completeness of 4-incidence colorability of semi-cubic graphs, Discrete Math. 308 (2008) 1334-1340. doi: 10.1016/j.disc.2007.03.076

[17] M. Maydanskiy, The incidence coloring conjecture for graphs of maximum degree three, Discrete Math. 292 (2005) 131-141. doi: 10.1016/j.disc.2005.02.003

[18] A.C. Shiau, T.-H. Shiau and Y.-L. Wang, Incidence coloring of Cartesian product graphs, Inform. Process. Lett. 115 (2015) 765-768. doi: 10.1016/j.ipl.2015.05.002

[19] W.C. Shiu and P.K. Sun, Invalid proofs on incidence coloring, Discrete Math. 308 (2008) 6575-6580. doi: 10.1016/j.disc.2007.11.030