Paper Info
Title
Supereulerian graphs with width s and s-collapsible graphs.
Abstract
For an integer s>0 and for u,v∈V(G) with u≠v, an (s;u,v)-trail-system of G is a subgraph H consisting of s edge-disjoint (u,v)-trails. A graph is supereulerian with widths if for any u,v∈V(G) with u≠v, G has a spanning (s;u,v)-trail-system. The supereulerian widthμ′(G) of a graph G is the largest integer s such that G is supereulerian with width k for every integer k with 0≤k≤s. Thus a graph G with μ′(G)≥2 has a spanning Eulerian subgraph. Catlin (1988) introduced collapsible graphs to study graphs with spanning Eulerian subgraphs, and showed that every collapsible graph G satisfies μ′(G)≥2 (Catlin, 1988; Lai et al., 2009). Graphs G with μ′(G)≥2 have also been investigated by Luo et al. (2006) as Eulerian-connected graphs. In this paper, we extend collapsible graphs to s-collapsible graphs and develop a new related reduction method to study μ′(G) for a graph G. In particular, we prove that K3,3 is the smallest 3-edge-connected graph with μ′<3. These results and the reduction method will be applied to determine a best possible degree condition for graphs with supereulerian width at least 3, which extends former results in Catlin (1988) and Lai (1988).
Year
DOI
Venue
2016
10.1016/j.dam.2015.07.013
Discrete Applied Mathematics
Keywords
Field
DocType
Supereulerian graphs,Collapsible graphs,Edge-connectivity,Edge-disjoint trails,Supereulerian graphs with width s,The supereulerian width of a graph,s-collapsible graphs,Eulerian-connected graphs
Integer,Discrete mathematics,Graph,Indifference graph,Combinatorics,Chordal graph,Eulerian path,Pathwidth,1-planar graph,Mathematics
Journal
Volume
ISSN
Citations 
200
0166-218X
2
PageRank 
References 
Authors
0.40
14
5
Name
Order
Citations
PageRank
Ping Li1217.14
Hao Li252.52
Ye Chen3667.20
Herbert Fleischner422435.35
Hong-Jian Lai563197.39