منابع مشابه
Two-ended regular median graphs
We show that regular median graphs of linear growth are the Cartesian product of finite hypercubes with the two-way infinite path. Such graphs are Cayley graphs and have only two ends. For cubic median graphs G the condition of linear growth can be weakened to the condition that G has two ends. For higher degree the relaxation to twoended graphs is not possible, which we demonstrate by an examp...
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We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime g...
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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...
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An easy count ing argument shows here that la(G)>f . f f t " d i f f icu l ty is in establishing the upper bound. This problem has received much attention; see Alon [1]. We show here how Alon's beautiful treatment for graphs with large girth allows us easily to handle random regular graphs. By the random regular graph G,,, (where rn is even) we mean a graph picked uniformly at random from the s...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.01.012