2022/05/18 by Morteza Hasanvand, Hasanvand, Morteza
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2205.09038
openalex publication_date 2022/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1976 Frank and Gyárfás gave a necessary and sufficient condition for the existence of an orientation in an arbitrary graph G such that for each vertex v, the out-degree d+G(v) of it satisfies p(v)≤ d+G(v)≤ q(v), where p and q are two integer-valued functions on V(G) with p≤ q. In this paper, we give a sufficient edge-connectivity condition for the existence of an orientation in G such that for each vertex v, d+G(v)∈ \p(v),q(v)\, provided that for each vertex v, p(v)≤ (1)/(2)dG(v) ≤ q(v), |q(v)-p(v)|≤ k, and there is t(v)∈ \p(v),q(v)\ in which |E(G)|=∑v∈ V(G)t(v). This result is a generalization of a theorem due to Thomassen (2012) on the existence of modulo orientations in highly edge-connected graphs.