Geodesic
Conflict-Free Vertex-Connections of Graphs
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 51-65

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

A path in a vertex-colored graph is called conflict-free if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be conflict-free vertex-connected if any two vertices of the graph are connected by a conflict-free path. This paper investigates the question: for a connected graph G, what is the smallest number of colors needed in a vertex-coloring of G in order to make G conflict-free vertex-connected. As a result, we get that the answer is easy for 2-connected graphs, and very difficult for connected graphs with more cut-vertices, including trees.
Keywords: vertex-coloring, conflict-free vertex-connection, 2-connected graph, tree 
@article{DMGT_2020_40_1_a3,
     author = {Li, Xueliang and Zhang, Yingying and Zhu, Xiaoyu and Mao, Yaping and Zhao, Haixing and Jendrol{\textquoteright}, Stanislav},
     title = {Conflict-Free {Vertex-Connections} of {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {51--65},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a3/}
}
TY  - JOUR
AU  - Li, Xueliang
AU  - Zhang, Yingying
AU  - Zhu, Xiaoyu
AU  - Mao, Yaping
AU  - Zhao, Haixing
AU  - Jendrol’, Stanislav
TI  - Conflict-Free Vertex-Connections of Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2020
SP  - 51
EP  - 65
VL  - 40
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a3/
LA  - en
ID  - DMGT_2020_40_1_a3
ER  - 
%0 Journal Article
%A Li, Xueliang
%A Zhang, Yingying
%A Zhu, Xiaoyu
%A Mao, Yaping
%A Zhao, Haixing
%A Jendrol’, Stanislav
%T Conflict-Free Vertex-Connections of Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2020
%P 51-65
%V 40
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a3/
%G en
%F DMGT_2020_40_1_a3
Li, Xueliang; Zhang, Yingying; Zhu, Xiaoyu; Mao, Yaping; Zhao, Haixing; Jendrol’, Stanislav. Conflict-Free Vertex-Connections of Graphs. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 51-65. http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a3/