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A nonincreasing sequence of nonnegative integers is a graphic sequence if it is realizable by a simple graph on vertices. In this case, is referred to as a realization of . Given two graphs and , A. Busch et al. (2014) introduced the potential-Ramsey number of and , denoted by , as the smallest nonnegative integer such that for every -term graphic sequence , there is a realization of with or with , where is the complement of . For and , let be the graph obtained...
Let be the complete bipartite graph with partite sets and . A split bipartite-graph on vertices, denoted by , is the graph obtained from by adding new vertices , such that each of is adjacent to each of and each of is adjacent to each of . Let and be nonincreasing lists of nonnegative integers, having lengths and , respectively. The pair is potentially -bigraphic if there is a simple bipartite graph containing (with vertices in the part of size and vertices...
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