Regular Spanning Subgraphs of Bipartite Graphs of High Minimum Degree

Regular Spanning Subgraphs of Bipartite Graphs of High Minimum Degree

Let G be a simple balanced bipartite graph on 2n vertices, δ = δ(G)/n, and ρ0 = δ+ √ 2δ−1 2 . If δ ≥ 1/2 then G has a ⌊ρ0n⌋-regular spanning subgraph. The statement is nearly tight.

Minimum Face-Spanning Subgraphs of Plane Graphs

A plane graph is a planar graph with a fixed embedding. Let G = (V,E) be an edge weighted connected plane graph, where V and E are the set of vertices and edges, respectively. Let F be the set of faces of G. For each edge e ∈ E, let w(e) ≥ 0 be the weight of the edge e of G. A face-spanning subgraph of G is a connected subgraph H induced by a set of edges S ⊆ E such that the vertex set of H con...

Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree

Let F be a family of graphs and let d be large enough. For every d-regular graph G, we study the existence of a spanning F -free subgraph of G with large minimum degree. This problem is wellunderstood if F does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs. To prove these results, we s...

Decompositions of Complete Graphs into Bipartite 2-Regular Subgraphs

It is shown that if G is any bipartite 2-regular graph of order at most n2 or at least n − 2, then the obvious necessary conditions are sufficient for the existence of a decomposition of the complete graph of order n into a perfect matching and edge-disjoint copies of G.

A Note on Degree-Constrained Star Subgraphs of Bipartite Graphs