3-Trees in polyhedral maps

Autor:	David Barnette
Rok vydání:	1992
Předmět:	Combinatorics Discrete mathematics Polyhedron Steinitz's theorem General Mathematics Mathematics::Metric Geometry Balinski's theorem Polytope Projective plane Tree (graph theory) Klein bottle Polyhedral graph Mathematics
Zdroj:	Israel Journal of Mathematics. 79:251-256
ISSN:	1565-8511 0021-2172
DOI:	10.1007/bf02808218
Popis:	We show that the vertices of the graph of any polyhedral map on the projective plane, torus or Klein bottle can be covered by a subgraph that is a tree of maximum valence 3. This extends a theorem of the author, who previously proved this theorem for the graphs of 3-dimensional polytopes. Several theorems dealing with paths in polyhedral maps are a consequence of these theorems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::dc11b5e563a9842dc3262c39068e8f56 https://doi.org/10.1007/bf02808218 Zobrazit plný text záznamu Full text from SpringerLink