On locating cubic subgraphs in bounded-degree connected bipartite graphs

A Note on Degree-Constrained Star Subgraphs of Bipartite Graphs

Decomposing Cubic Graphs into Connected Subgraphs of Size Three

Let S = {K1,3,K3, P4} be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph G into graphs taken from any non-empty S′ ⊆ S. The problem is known to be NP-complete for any possible choice of S′ in general graphs. In this paper, we assume that the input graph is cubic, and study the computational complexity of the problem of partitioning its edge se...

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.

Dominating Bipartite Subgraphs in Graphs

A graph G is hereditarily dominated by a class D of connected graphs if each connected induced subgraph of G contains a dominating induced subgraph belonging to D. In this paper we characterize graphs hereditarily dominated by classes of complete bipartite graphs, stars, connected bipartite graphs, and complete k-partite graphs.

On Dominating Even Subgraphs in Cubic Graphs

It is known that a 3-edge-connected graph has a spanning even subgraph in which every component contains at lest five vertices, and the lower bound is best possible. A natural question arises whether we can improve the lower bound by changing the spanning property with the dominating property. In this paper, we show that a 3-edge-connected cubic graph has a dominating even subgraph in which eve...