منابع مشابه
Stable Roommates Matchings, Mirror Posets, Median Graphs, and the Local/Global Median Phenomenon in Stable Matchings
For stable marriage (SM) and solvable stable roommates (SR) instances, it is known that there are stable matchings that assign each participant to his or her (lower/upper) median stable partner. Moreover, for SM instances, a stable matching has this property if and only if it is a median of the distributive lattice formed by the instance’s stable matchings. In this paper, we show that the above...
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 کاملPosets and planar graphs
Usually dimension should be an integer valued parameter. We introduce a refined version of dimension for graphs, which can assume a value 1⁄2 t 1l t , thought to be between t 1 and t. We have the following two results: (a) a graph is outerplanar if and only if its dimension is at most 1⁄22l3 . This characterization of outerplanar graphs is closely related to the celebrated result of W. Schnyder...
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 کاملPosets and VPG Graphs
We investigate the class of intersection graphs of paths on a grid (VPG graphs), and specifically the relationship between the bending number of a cocomparability graph and the poset dimension of its complement. We show that the bending number of a cocomparability graph G is at most the poset dimension of the complement of G minus one. Then, via Ramsey type arguments, we show our upper bound is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90140-o