Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871230 | Discrete Applied Mathematics | 2018 | 9 Pages |
Abstract
Consider a graph G in which the longest path has order |V(G)|â1. We denote the number of vertices v in G such that Gâv 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)|â1 vertices, the answer to Gallai's question is positive iff tGâ 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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Gábor Wiener, Carol T. Zamfirescu,