Paper Info
Title
Excluding a large theta graph.
Abstract
A theta graph, denoted θa,b,c, is a graph of order a+b+c−1 consisting of a pair of vertices and three internally-disjoint paths between them of lengths a, b, and c. In this paper we study graphs that do not contain a large θa,b,c minor. More specifically, we describe the structure of θ1,2,t-, θ2,2,t-, θ1,t,t-, θ2,t,t-, and θt,t,t-free graphs where t is large. The main result is a characterization of θt,t,t-free graphs for large t. The 3-connected θt,t,t-free graphs are formed by 3-summing graphs without a long path to certain planar graphs. The 2-connected θt,t,t-free graphs are then built up in a similar fashion by 2- and 3-sums. This result implies a well-known theorem of Robertson and Chakravarti on graphs that do not have a bond containing three specified edges.
Year
DOI
Venue
2018
10.1016/j.jctb.2018.03.002
Journal of Combinatorial Theory, Series B
Keywords
Field
DocType
Theta graphs,Graph minors
Graph,Discrete mathematics,Combinatorics,Vertex (geometry),Theta graph,Mathematics,Planar graph
Journal
Volume
ISSN
Citations 
132
0095-8956
0
PageRank 
References 
Authors
0.34
7
2
Name
Order
Citations
PageRank
Guoli Ding144451.58
Emily A. Marshall202.03