Proper orientation number of triangle-free bridgeless outerplanar graphs. / Ai, Jiangdong; Gerke, Stefanie; Gutin, Gregory; Shi, Yongtang; Taoqiu, Zhenyu.

In: Journal of Graph Theory, 18.03.2020.

Research output: Contribution to journalArticle

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Proper orientation number of triangle-free bridgeless outerplanar graphs. / Ai, Jiangdong; Gerke, Stefanie; Gutin, Gregory; Shi, Yongtang; Taoqiu, Zhenyu.

In: Journal of Graph Theory, 18.03.2020.

Research output: Contribution to journalArticle

APA

Ai, J., Gerke, S., Gutin, G., Shi, Y., & Taoqiu, Z. (Accepted/In press). Proper orientation number of triangle-free bridgeless outerplanar graphs. Journal of Graph Theory.

BibTeX

@article{3b7b4394d04944d8a47365c6c538107f,
title = "Proper orientation number of triangle-free bridgeless outerplanar graphs",
abstract = "An orientation of a graph G is a digraph obtained from G by replacing each edge by exactly one of two possible arcs with the same endpoints. We call an orientation proper if neighbouring vertices have different in-degrees. The proper orientation number of a graph G, denoted by \chi(G), is the minimum maximum in-degree of a proper orientation of G. Araujo et al. (Theor. Comput. Sci. 639 (2016) 14--25) asked whether there is a constant c such that \chi(G)< c for every outerplanar graph $G$ and showed that \chi}(G) <= 7$for every cactus G. We prove that \chi}(G) <=3 if G is a triangle-free 2-connected outerplanar graph and$\chi (G) <= 4$if G is a triangle-free bridgeless outerplanar graph. ", author = "Jiangdong Ai and Stefanie Gerke and Gregory Gutin and Yongtang Shi and Zhenyu Taoqiu", year = "2020", month = mar day = "18", language = "English", journal = "Journal of Graph Theory", issn = "0364-9024", publisher = "Wiley-Liss Inc.", } RIS TY - JOUR T1 - Proper orientation number of triangle-free bridgeless outerplanar graphs AU - Ai, Jiangdong AU - Gerke, Stefanie AU - Gutin, Gregory AU - Shi, Yongtang AU - Taoqiu, Zhenyu PY - 2020/3/18 Y1 - 2020/3/18 N2 - An orientation of a graph G is a digraph obtained from G by replacing each edge by exactly one of two possible arcs with the same endpoints. We call an orientation proper if neighbouring vertices have different in-degrees. The proper orientation number of a graph G, denoted by \chi(G), is the minimum maximum in-degree of a proper orientation of G. Araujo et al. (Theor. Comput. Sci. 639 (2016) 14--25) asked whether there is a constant c such that \chi(G)< c for every outerplanar graph$G$and showed that \chi}(G) <= 7$ for every cactus G. We prove that \chi}(G) <=3 if G is a triangle-free 2-connected outerplanar graph and $\chi (G) <= 4$ if G is a triangle-free bridgeless outerplanar graph.

AB - An orientation of a graph G is a digraph obtained from G by replacing each edge by exactly one of two possible arcs with the same endpoints. We call an orientation proper if neighbouring vertices have different in-degrees. The proper orientation number of a graph G, denoted by \chi(G), is the minimum maximum in-degree of a proper orientation of G. Araujo et al. (Theor. Comput. Sci. 639 (2016) 14--25) asked whether there is a constant c such that \chi(G)< c for every outerplanar graph $G$ and showed that \chi}(G) <= 7$for every cactus G. We prove that \chi}(G) <=3 if G is a triangle-free 2-connected outerplanar graph and$\chi (G) <= 4\$ if G is a triangle-free bridgeless outerplanar graph.

M3 - Article

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

ER -