A partition of connected graphs

dc.creatorWiseman, Gus
dc.date2005-05-09
dc.date.accessioned2026-07-07T05:19:44Z
dc.date.available2026-07-07T05:19:44Z
dc.descriptionWe define an algorithm k which takes a connected graph G on a totally ordered vertex set and returns an increasing tree R (which is not necessarily a subtree of G). We characterize the set of graphs G such that k(G)=R. Because this set has a simple structure (it is isomorphic to a product of non-empty power sets), it is easy to evaluate certain graph invariants in terms of increasing trees. In particular, we prove that, up to sign, the coefficient of x^q in the chromatic polynomial of G is the number of increasing forests with q components that satisfy a condition that we call G-connectedness. We also find a bijection between increasing G-connected trees and broken circuit free subtrees of G.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0505155
dc.identifierhttp://arxiv.org/abs/math/0505155
dc.identifierElectronic J. Combinatorics 12, N1 (2005), 8pp
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75124
dc.subjectCombinatorics
dc.subject05C30, 05C05
dc.titleA partition of connected graphs
dc.typetext

Files

Collections