منابع مشابه
A simple axiomatization of the median procedure on median graphs
A profile π = (x1, ..., xk), of length k, in a finite connected graph G is a sequence of vertices of G, with repetitions allowed. A median x of π is a vertex for which the sum of the distances from x to the vertices in the profile is minimum. The median function finds the set of all medians of a profile. Medians are important in location theory and consensus theory. A median graph is a graph fo...
متن کاملA tight axiomatization of the median procedure on median graphs
Aprofileπ = (x1, . . . , xk), of length k, in a finite connected graphG is a sequence of vertices ofG, with repetitions allowed. Amedian x ofπ is a vertex forwhich the sumof the distances from x to the vertices in the profile is minimum. The median function finds the set of all medians of a profile. Medians are important in location theory and consensus theory. A median graph is a graph for whi...
متن کاملOn Median Graphs and Median Grid Graphs on Median Graphs and Median Grid Graphs
Let e be an edge of a median graph G which is contained in exactly one 4-cycle. Then it is proved that G n e is a median graph. The converse holds as well provided that e is not contained is a subgraph isomorphic to the 3-cube minus a vertex. These results are used to give several characterizations of median grid graphs. (Grid graphs are subgraphs of complete grids, i.e. of the Cartesian produc...
متن کاملOn median graphs and median grid graphs
Let G be a Q4-free median graph on n vertices and m edges. Let k be the number of equivalence classes of Djoković-Winkler’s relation Θ and let h be the number of Q3’s in G. Then we prove that 2n −m − k + h = 2. We also characterize median grid graphs in several different ways, for instance, they are the grid graphs with m− n + 1 squares. To obtain these results we introduce the notion of square...
متن کاملThe p-median and p-center Problems on Bipartite Graphs
Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1998
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(98)00003-1