Add to ORKGPlayers A and B alternatively colour edges of a graph G, red and blue respectively. Let Lsym(G) be the largest number of moves during which B can keep the red and blue subgraphs isomorphic, no matter how A plays. This function was introduced by Harary, Slany and Verbitsky who in particular showed that for complete bipartite graphs we have Lsym(Km;n) = mn 2 if mn is even and that Lsym(K2m+1;2n+1) ¸ max(m;n). Here we prove that Lsym(K2m+1;2n+1) = O(n); if m · n · mO(1), answering a question posed by Harary, Slany and Verbitsky. 1
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AbstractThis paper is partitioned into two parts. In the first part we determine the maximum number ...
AbstractWe call a bipartite graph homogeneous if every finite partial automorphism which respects le...
AbstractGiven a graph G, we consider a game where two players, A and B, alternatingly color edges of...
For each s ≥ 2, there exists m0 such that the following holds for all m ≥ m0: Let G be a bipartite g...
AbstractFor arbitrary odd prime power q and s ∈ (0, 1] such that qs is an integer, we construct a do...
Abstract: "We call a bipartite graph homogeneous if every finite partial automorphism which respects...
summary:Given a graph $G$, let $f(G)$ denote the maximum number of edges in a bipartite subgraph of ...
AbstractHarary, Robinson and Wormald (1978) proved that for a complete tripartite graph G = K (m, n,...
AbstractLet f(k) be the largest number such that each k-regular bipartite graph with 2n vertices has...
Graphs and AlgorithmsThe following problem was solved by Woodall in 1972: for any pair of nonnegativ...
One of the cornerstones of extremal graph theory is a result of Füredi, later reproved and given due...
the original bipartite graph B and denote the complement ¯ B as G. proof. Independent sets in B corr...
We are interested in finding symmetries in graphs and then use these symmetries for graph drawing al...
Let it (G) be the number of independent sets of size t in a graph G. Engbers and Galvin asked how la...
AbstractThe bipartite regulation number br(G) of a bipartite graph G with maximum degree d is the mi...
AbstractThis paper is partitioned into two parts. In the first part we determine the maximum number ...
AbstractWe call a bipartite graph homogeneous if every finite partial automorphism which respects le...