Placing Two Edge-disjoint Copies of a Tree into a Bipartite Graph

Hui Li and Yunshu Gao

Applied Mathematics and Computation, 2023, vol. 452, issue C

Abstract: We state that τ is an embedding of bipartite graph G(X0,X1) in the complete bipartite graph Bn(Y0,Y1) provided τ:V(G)→V(Bn), with σ(Xi)⊆Yi(i=0,1). Suppose that there are two embeddings of G in Bn such that both imagines under these two embeddings are edge-disjoint, we called that there is 2-packing of G in Bn. Let G(X1,X2) be a bipartite graph. For i=1,2, we use Δi to denote the maximum degree of the vertex in Xi. Let T(V1,V2) be a tree of order n with |V1|=a and |V2|=b. We demonstrate that if b≥a−1, there exists a 2-packing (σ,τ) of T in some Bn+1 such that Δ2(σ(T)∪τ(T))≤Δ2(T)+2. In general, Δ2(T)+2 can not be reduced to Δ2(T)+1, making this result sharp.

Keywords: Embedding; 2-packing; Tree decomposition (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:452:y:2023:i:c:s009630032300214x

DOI: 10.1016/j.amc.2023.128045

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