Journal ArticleDOI
Graph reconstruction—a survey
J. A. Bondy,Robert L. Hemminger +1 more
Reads0
Chats0
TLDR
The progress made on the Reconstruction Conjecture is reviewed, up to isomorphism, since it was first formulated in 1941 and a number of related questions are discussed.Abstract:
The Reconstruction Conjecture asserts that every finite simple undirected graph on three or more vertices is determined, up to isomorphism, by its collection of vertex-deleted subgraphs. This article reviews the progress made on the conjecture since it was first formulated in 1941 and discusses a number of related questions.read more
Citations
More filters
Book
Graph theory with applications
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Book
Graph Coloring Problems
Tommy R. Jensen,Bjarne Toft +1 more
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
Journal ArticleDOI
Aromaticity of polycyclic conjugated hydrocarbons.
TL;DR: Theoretical Approach to Chemical Structure, Approximate Approaches versus Ambitious Computations, and Use of Signed Matrices.
Journal ArticleDOI
On the combinatorial problems which I would most like to see solved
TL;DR: I was asked to write a paper about the major unsolved problems in com-binatorial mathematics, but after some thought it seemed better to modify the title to a less pretentious one, so I state only my three favourite problems.
Book
Topics in Graph Automorphisms and Reconstruction
Josef Lauri,Raffaele Scapellato +1 more
TL;DR: In this paper, the authors present an in-depth coverage of important areas of graph theory maintaining a focus on symmetry properties of graphs, including graph automorphisms and the reconstruction problem.
References
More filters
Journal ArticleDOI
A congruence theorem for trees.
TL;DR: In this paper, it is shown that if there is a one-to-one correspondence in type, and frequency of type, between the subgraphs of order n − lmA and J5, that is, if there exists a labeling such that φ ^ ) ^ cφi), i = l, 2, •••, n, then A ~ B.
Journal ArticleDOI
The falsity of the reconstruction conjecture for tournaments
TL;DR: The conjecture that for all sufficiently large p any tournament of order p is uniquely reconstructable from its point-deleted subtournaments is shown to be false.
Journal ArticleDOI
A note on the line reconstruction problem
TL;DR: In this paper, a finite, undirected graph without loops or multiple lines is defined, and the sets of points and lines of the graph are defined as sets of vertices and edges.
Journal ArticleDOI
Infinite graphs—A survey
TL;DR: In this paper, an expository article describes work which has been done on various problems involving infinite graphs, mentioning also a few unsolved problems or suggestions for future investigation, including the problem of infinite graphs.