Spanning Eulerian subgraphs of bounded degree in triangulations
type: Item
instance of: scholarly article
title: Spanning Eulerian subgraphs of bounded degree in triangulations
zbMATH Open document ID: 0804.05026
DOI: 10.1007/BF02986656
author: Nicholas Wormald
author: Zhicheng Gao
published in: Graphs and Combinatorics
publication date: 1994-09-26T00:00:00Z
review text: A closed \(k\)-trail is a spanning Eulerian subgraph with maximum degree at most \(2k\). The main result states that every triangulation of a disk or an annulus has a closed 4-trail. Since every triangulation in the projective plane, the torus and the Klein bottle has a spanning subgraph which triangulates an annulus, this implies that all triangulations in the projective plane, the torus and the Klein bottle have closed 4- trails. The same holds for 5-connected triangulations in the double-torus with representativity at least 6.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 644729
zbMATH Keywords: \(k\)-trail
zbMATH Keywords: spanning Eulerian subgraph
zbMATH Keywords: triangulation
zbMATH Keywords: projective plane
zbMATH Keywords: torus
zbMATH Keywords: Klein bottle
reviewed by: Stelian Mihalas
MaRDI profile type: Publication
cites work: Trees in Polyhedral Graphs
cites work: Spanning planar subgraphs of graphs in the torus and Klein bottle
cites work: Hamiltonicity of 5‐Connected Toroidal Triangulations
cites work: Spanning trees in locally planar triangulations
cites work: Computing the orientable genus of projective graphs
cites work: 2-walks in circuit graphs
cites work: Q4014627
cites work: Q3686751
cites work: 4-connected projective planar graphs are Hamiltonian
cites work: Five-connected toroidal graphs are Hamiltonian
cites work: A theorem on paths in planar graphs
cites work: Trees in triangulations
cites work: A Theorem on Planar Graphs
cites work: Bridges and Hamiltonian circuits in planar graphs
description: scientific article; zbMATH DE number 644729