2019/06/10 by Morteza Hasanvand, Hasanvand, Morteza · 1 citation
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1906.04325
openalex publication_date 2019/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we show that every (3k-3)-edge-connected graph G, under a certain condition on whose degrees, can be edge-decomposed into k factors G1,…, Gk such that for each vertex v∈ V(Gi), |dGi(v)-dG(v)/k|< 1, where 1≤ i≤ k. As application, we deduce that every 6-edge-connected graph G can be edge-decomposed into three factors G1, G2, and G3 such that for each vertex v∈ V(Gi), |dGi(v)-dG(v)/3|< 1, unless G has exactly one vertex z with dG(z) \stackrel3\not≡0. Next, we show that every odd-(3k-2)-edge-connected graph G can be edge-decomposed into k factors G1,…, Gk such that for each vertex v∈ V(Gi), dGi(v) and dG(v) have the same parity and |dGi(v)-dG(v)/k|< 2, where k is an odd positive integer and 1≤ i≤ k. Finally, we give a sufficient edge-connectivity condition for a graph G to have a parity factor F with specified odd-degree vertices such that for each vertex v, | dF(v)-ε dG(v)|< 2, where ε is a real number with 0< ε < 1.