The extremal function for partial bipartite tilings

The extremal function for partial bipartite tilings

Note on Bipartite Graph Tilings

Let s < t be two fixed positive integers. We determine sufficient minimum degree conditions for a bipartite graph G, with both color classes of size n = k(s + t), which ensure that G has a Ks,t-factor. Our result extends the work of Zhao, who determined the minimum degree threshold which guarantees that a bipartite graph has a Ks,s-factor.

An Extremal Problem for Complete Bipartite Graphs

Define f(n, k) to be the largest integer q such that for every graph G of order n and size q, G contains every complete bipartite graph K u, ,, with a+h=n-k . We obtain (i) exact values for f(n, 0) and f(n, 1), (ii) upper and lower bounds for f(n, k) when ku2 is fixed and n is large, and (iii) an upper bound for f(n, lenl) .

Det-extremal cubic bipartite graphs

Let G be a connected k–regular bipartite graph with bipartition V (G) = X ∪Y and adjacency matrix A. We say G is det–extremal if per(A) = |det(A)|. Det–extremal k–regular bipartite graphs exist only for k = 2 or 3. McCuaig has characterized the det–extremal 3–connected cubic bipartite graphs. We extend McCuaig’s result by determining the structure of det–extremal cubic bipartite graphs of conne...

Extremal bipartite graphs with high girth

Let us denote by EX (m,n; {C4, . . . , C2t}) the family of bipartite graphs G with m and n vertices in its classes that contain no cycles of length less than or equal to 2t and have maximum size. In this paper the following question is proposed: does always such an extremal graph G contain a (2t + 2)-cycle? The answer is shown to be affirmative for t = 2, 3 or whenever m and n are large enough ...