Paper Info
Title
Gallai's question and constructions of almost hypotraceable graphs.
Abstract
Consider a graph G in which the longest path has order |V(G)|−1. We denote the number of vertices v in G such that G−v is non-traceable with tG. Gallai asked in 1966 whether, in a connected graph, the intersection of all longest paths is non-empty. Walther showed that, in general, this is not true. In a graph G in which the longest path has |V(G)|−1 vertices, the answer to Gallai’s question is positive iff tG≠0. In this article we study almost hypotraceable graphs, which constitute the extremal case tG=1. We give structural properties of these graphs, establish construction methods for connectivities 1 through 4, show that there exists a cubic 3-connected such graph of order 28, and draw connections to works of Thomassen and Gargano et al.
Year
DOI
Venue
2018
10.1016/j.dam.2018.02.017
Discrete Applied Mathematics
Keywords
Field
DocType
Gallai’s problem,Traceable,Hypotraceable,Almost hypotraceable
Discrete mathematics,Graph,Combinatorics,Existential quantification,Vertex (geometry),Connectivity,Longest path problem,Mathematics
Journal
Volume
ISSN
Citations 
243
0166-218X
0
PageRank 
References 
Authors
0.34
15
2
Name
Order
Citations
PageRank
Gábor Wiener16410.65
Carol T. Zamfirescu23815.25