We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a bipartite distance hereditary graph. Relations with the class of Ptolemaic graphs are discussed and exploited to give an alternative proof of the result.
On the Galois Lattice of Bipartite Distance Hereditary Graphs / Apollonio, Nicola; M., Caramia; Franciosa, Paolo Giulio. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - STAMPA. - 190-191:(2015), pp. 13-23. [10.1016/j.dam.2015.03.014]
On the Galois Lattice of Bipartite Distance Hereditary Graphs
APOLLONIO, Nicola;FRANCIOSA, Paolo Giulio
2015
Abstract
We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a bipartite distance hereditary graph. Relations with the class of Ptolemaic graphs are discussed and exploited to give an alternative proof of the result.| File | Dimensione | Formato | |
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