Journal•ISSN: 0911-0119
Graphs and Combinatorics
Springer Science+Business Media
About: Graphs and Combinatorics is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Mathematics & Combinatorics. It has an ISSN identifier of 0911-0119. Over the lifetime, 2800 publications have been published receiving 28419 citations.
Papers published on a yearly basis
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TL;DR: Lethr(n) denote the maximum number of edges in anr-uniform hypergraph onn vertices and in which the union of any three edges has size greater than 3r − 3.
Abstract: LetH be a fixed graph of chromatic numberr. It is shown that the number of graphs onn vertices and not containingH as a subgraph is $$2^{(\begin{array}{*{20}c} n \\ 2 \\ \end{array} )(1 - \frac{1}{{r - 1}} + o(1))} $$ . Leth r (n) denote the maximum number of edges in anr-uniform hypergraph onn vertices and in which the union of any three edges has size greater than 3r ? 3. It is shown thath r (n) =o(n 2) although for every fixedc < 2 one has lim n?? h r (n)/n c = ?.
321 citations
TL;DR: Upper and lower bounds on the diameter and the mean distance inG in terms ofλ2, the second smallest eigenvalue of the difference Laplacian matrix of a graphG, are derived.
Abstract: It is well-known that the second smallest eigenvalue? 2 of the difference Laplacian matrix of a graphG is related to the expansion properties ofG. A more detailed analysis of this relation is given. Upper and lower bounds on the diameter and the mean distance inG in terms of? 2 are derived.
319 citations
TL;DR: It is shown that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete.
Abstract: We show that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete. Furthermore, we show direct equivalences between these three types of puzzles: any puzzle of one type can be converted into an equivalent puzzle of any other type.
241 citations
TL;DR: This article is intended as a survey, updating earlier surveys in the area and contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs and digraphs.
Abstract: This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs and digraphs.
227 citations
TL;DR: This survey attempts to bring together most of the results and papers that dealt with the concept of rainbow connection, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity.
Abstract: The concept of rainbow connection was introduced by Chartrand et al. [14] in 2008. It is interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers that dealt with it. We begin with an introduction, and then try to organize the work into five categories, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity. This survey also contains some conjectures, open problems and questions.
207 citations