Packing k-edge Trees in Graphs of Restricted Vertex Degrees

dc.creatorKelmans, Alexander
dc.date2006-10-11
dc.date.accessioned2026-07-07T07:28:59Z
dc.date.available2026-07-07T07:28:59Z
dc.descriptionLet v(G) be the number of vertices and t(G,k) the maximum number of disjoint k-edge trees in G. In this paper we show that (a1) if G is a graph with every vertex of degree at least two and at most s, where s > 3, then t(G,2) is at least v(G)/(s+1), (a2) if G is a graph with every vertex of degree at least two and at most 3 and G has no 5-vertex components, then t(G,2) is at least v(G)/4, (a3) if G is a graph with every vertex of degree at least one and at most s and G has no k--vertex component, where k >1 and s > 2, then t(G,k) is at least (v(G) - k)/(sk - k +1), and (a4) the above bounds are attained for infinitely many connected graphs. Our proofs provide polynomial time algorithms for finding the corresponding packings in a graph. Keywords: subgraph packing, 2-edge and k-edge paths, k-edge trees, polynomial time approximation algorithms.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0610384
dc.identifierhttp://arxiv.org/abs/math/0610384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117933
dc.subjectCombinatorics
dc.subject05C10
dc.titlePacking k-edge Trees in Graphs of Restricted Vertex Degrees
dc.typetext

Files

Collections