2015/11/10 by Nicola Apollonio, Massimiliano Caramia, Apollonio, Nicola +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1511.03100
arxiv created 2015/11/10 · openalex publication_date 2015/11/10 · arxiv updated 2015/11/11 · openalex created_date 2022/02/25 · openalex updated_date 2026/07/28
Bandelt and Mulder's structural characterization of Bipartite Distance Hereditary graphs asserts that such graphs can be built inductively starting from a single vertex and by repeatedly adding either pending vertices or twins (i.e., vertices with the same neighborhood as an existing one). Dirac and Duffin's structural characterization of 2-connected series-parallel graphs asserts that such graphs can be built inductively starting from a single edge by adding either edges in series or in parallel. In this paper we prove that the two constructions are the same construction when bipartite graphs are viewed as the fundamental graphs of a graphic matroid. We then apply the result to re-prove known results concerning bipartite distance hereditary graphs and series-parallel graphs, to characterize self-dual outer-planar graphs and, finally, to provide a new class of polynomially-solvable instances for the integer multi commodity flow of maximum value.