Geometric versions of Ramsey-type and Turán-type problems are studied in a special but natural representation of bipartite graphs and similar questions are asked for general representations. A bipartite geometric graphG(m,n) = [A,B] is simple if the vertex classes A,B of G(m,n) are represented in R2 as A = {(1, 0), (2, 0), . . . , (m, 0)}, B = {(1, 1), (2, 1), . . . , (n, 1)} and the edge ab is...

Unavoidable subgraphs have been widely studied in the context of Ramsey Theory. The research in this area focuses on highly structured graphs such as cliques, cycles, paths, stars, trees, and wheels. We propose to study maximum unavoidable subgraphs measuring the size in the number of edges. We computed maximum unavoidable subgraphs for graphs up to order nine via SAT solving and observed that ...

Nowadays, graph theory is one of the most exciting fields mathematics due to tremendous developments in modern technology, where it used many important applications. The orthogonal double cover (ODC) a branch and considered as special class decomposition. In this paper, we decompose complete bipartite graphs Kx,x by caterpillar using method ODCs. article also deals with constructing ODCs genera...

We previously looked at communities as simply dense subgraphs graphs, or as subgraphs such that each node has a large fraction of its edges inside. Another view, taken in [3], starts from the hubs and authorities model. It argues that a structure of densely linked hubs and authorities is a common feature of communities. Such a core, a dense bipartite graph, can be considered the “signature” of ...

• We obtain the upper bounds for number of edges in even-cycle-free subgraphs complete transposition graphs, which are a family bipartite and arctransitive graphs. A new auxiliary graphs related to constructed used order bounds. Ramsey-type result is obtained. Given G H , generalized Turán ex ( ) maximum an -free subgraph . In this paper, we asymptotic bound on C T n 2 ℓ any ≥ 3 where cycle len...