Spanning trees with nonseparating paths

Autor(es)

Fernandes, Cristina G. ^[1] ; Hernandez-Velez, Cesar ^[1] ; Lee, Orlando ^[2] ; de Pina, Jose C. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Estadual Campinas, Inst Comp, BR-13083852 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE MATHEMATICS; v. 339, n. 1, p. 365-374, JAN 6 2016.
• Citações Web of Science: 0

Resumo

We consider questions related to the existence of spanning trees in connected graphs with the property that, after the removal of any path in the tree, the graph remains connected. We show that, for planar graphs, the existence of trees with this property is closely related to the Hamiltonicity of the graph. For graphs with a 1- or 2-vertex cut, the Hamiltonicity also plays a central role. We also deal with spanning trees satisfying this property restricted to paths arising from fundamental cycles. The cycle space of a graph can be generated by the fundamental cycles of every spanning tree, and Tutte showed that, for a 3-connected graph, it can be generated by nonseparating cycles. We are also interested in the existence of a fundamental basis consisting of nonseparating cycles. (C) 2015 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 12/24597-3 - Problemas topológicos e estruturais em teoria dos grafos.
• Beneficiário: César Israel Hernández Vélez
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado