2,978 research outputs found
Almost spanning subgraphs of random graphs after adversarial edge removal
Let Delta>1 be a fixed integer. We show that the random graph G(n,p) with
p>>(log n/n)^{1/Delta} is robust with respect to the containment of almost
spanning bipartite graphs H with maximum degree Delta and sublinear bandwidth
in the following sense: asymptotically almost surely, if an adversary deletes
arbitrary edges in G(n,p) such that each vertex loses less than half of its
neighbours, then the resulting graph still contains a copy of all such H.Comment: 46 pages, 6 figure
Rainbow -connectivity of random bipartite graphs
A path in an edge-colored graph is called a rainbow path if no two edges
of the path are colored the same. The minimum number of colors required to
color the edges of such that every pair of vertices are connected by at
least internally vertex-disjoint rainbow paths is called the rainbow
-connectivity of the graph , denoted by . For the random graph
, He and Liang got a sharp threshold function for the property
. In this paper, we extend this result to the case of
random bipartite graph .Comment: 15 pages. arXiv admin note: text overlap with arXiv:1012.1942 by
other author
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