Proper orientation number of triangle‐free bridgeless outerplanar graphs
نویسندگان
چکیده
منابع مشابه
On the proper orientation number of bipartite graphs
An orientation of a graph G is a digraph D obtained from G by replacing each edge by exactly one of the two possible arcs with the same endvertices. For each v ∈ V (G), the indegree of v in D, denoted by d− D (v), is the number of arcs with head v in D. An orientation D of G is proper if d− D (u) 6= d− D (v), for all uv ∈ E(G). The proper orientation number of a graph G, denoted by − →χ (G), is...
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For a graph G, let τ(G) be the decycling number of G and c(G) be the number of vertex-disjoint cycles of G. It has been proved that c(G)≤ τ(G)≤ 2c(G) for an outerplanar graph G. An outerplanar graph G is called lower-extremal if τ(G)= c(G) and upper-extremal if τ(G)= 2c(G). In this paper, we provide a necessary and sufficient condition for an outerplanar graph being upper-extremal. On the other...
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Graph orientation is a well-studied area of graph theory. A proper orientation of a graph G = (V,E) is an orientationD of E(G) such that for every two adjacent vertices v and u, d D (v) 6= d D (u) where d D (v) is the number of edges with head v in D. The proper orientation number of G is defined as −→χ (G) = min D∈Γ max v∈V (G) d D (v) where Γ is the set of proper orientations of G. We have χ(...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2020
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22565