An upper bound for the Ramsey numbers r(K3,G)

AbstractThe Ramsey number r(H,G) is defined as the minimum N such that for any coloring of the edges of the N-vertex complete graph KN in red and blue, it must contain either a ŕed H or a blue G. In this paper we show that for any graph G without isolated vertices, r(K3,G)⩽2q+1 where G has q edges. In other words, any graph on 2q+1 vertices with independence number at most 2 contains every (isolate-free) graph on q edges. This establishes a 1980 conjecture of Harary. The result is best possible as a function of q

Some Known Results and an Open Problem of Tree - Wheel Graph Ramsey Numbers

There are many famous problems on finding a regular substructure in a sufficiently large combinatorial structure, one of them i.e. Ramsey numbers. In this paper we list some known results and an open problem on graph Ramsey numbers. In the special cases, we list to determine graph Ramsey numbers for trees versus wheel

Some Known Results and an Open Problem of Tree - Wheel Graph Ramsey Numbers

There are many famous problems on finding a regular substructure in a sufficiently large combinatorial structure, one of them i.e. Ramsey numbers. In this paper we list some known results and an open problem on graph Ramsey numbers. In the special cases, we list to determine graph Ramsey numbers for trees versus wheel