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

Research output: Contribution to journal › Article

Forthcoming

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

Research output: Contribution to journal › Article

Ai, J, Gerke, S, Gutin, G, Shi, Y & Taoqiu, Z 2020, 'Proper orientation number of triangle-free bridgeless outerplanar graphs', *Journal of Graph Theory*.

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*.

Ai J, Gerke S, Gutin G, Shi Y, Taoqiu Z. Proper orientation number of triangle-free bridgeless outerplanar graphs. Journal of Graph Theory. 2020 Mar 18.

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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",

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language = "English",

journal = "Journal of Graph Theory",

issn = "0364-9024",

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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 -