2024/10/06 by Myungho Choi, Choi, Myungho, Suh-Ryung Kim +1
Computer Science · Engineering · #05C20 #05C75 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2410.04379
openalex publication_date 2024/10/06 · openalex created_date 2024/10/12 · openalex updated_date 2026/07/28
We say that a digraph D is (i,j)-step competitive if any two vertices have an (i,j)-step common out-neighbor in D and that a graph G is (i,j)-step competitively orientable if there exists an (i,j)-step competitive orientation of G. In [Choi et al. Competitively orientable complete multipartite graphs. Discrete Mathematics, 345(9):112950, 2022], Choi et al. introduce the notion of competitive digraph and completely characterize competitively orientable complete multipartite graphs in terms of the sizes of its partite sets. Here, a competitive digraph means a (1,1)-step competitive digraph. In this paper, the result of Choi et al. has been extended to a general characterization of (i,j)-step competitively orientable complete multipartite graphs.