Topic
Threshold graph
About: Threshold graph is a research topic. Over the lifetime, 157 publications have been published within this topic receiving 6034 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1980
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
Abstract: Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition. New edition of the "Classic" book on the topic Wonderful introduction to a rich research area Leading author in the field of algorithmic graph theory Beautifully written for the new mathematician or computer scientist Comprehensive treatment
4,370 citations
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TL;DR: The main topics of this article are split graphs, their degree sequences, and the place of these "split partitions" at the top of the partially ordered set of graphic partitions.
Abstract: The main topics of this article are split graphs, their degree sequences, and the place of these "split partitions" at the top of the partially ordered set of graphic partitions. One application is that threshold covered partitions are unigraphic.
416 citations
TL;DR: A graph theoretic scheme to link overlapping clusters is proposed in terms of the maximal complete subgraph (MCS) of a threshold graph, which is defined for a set of overlapping clusters by a given threshold value.
68 citations
TL;DR: For all n ≥ 3, there exist n − 1 threshold graphs of order n 2, pairwise noncospectral, each equienergetic to K n 2 as mentioned in this paper.
65 citations
TL;DR: In this paper, it was shown that not every threshold graph is optimal in this sense, where K and S indicate complete and edgeless graphs, K 1,r indicates a star on r + 1 vertices, and ∪ indicates disjoint union, and + indicates complete disjunctive join.
Abstract: Among all simple graphs on n vertices and e edges, which ones have the largest sum of squares of the vertex degrees? It is easy to see that they must be threshold graphs, but not every threshold graph is optimal in this sense. Boesch et al. [Boesch et al., Tech Rep, Stevens Inst Tech, Hoboken NJ, 1990] showed that for given n and e there exists exactly one graph of the form G1(p,q,r) = Kp + (Sq ∪ K1,r) and exactly one G2(p,q,r) = $S_{p} \cup (K_{q} + \overline{K_{1,r}})$ and that one of them is optimal, where K and S indicate complete and edgeless graphs, K1,r indicates a star on r + 1 vertices, ∪ indicates disjoint union, and + indicates complete disjoint join. We specify a general threshold graph in the form G *1 (a,b,c,d, …) = Ka + (Sb ∪ (Kc + (Sd ∪ ···))) or its complement G *2(a,b,c,d, …), and we prove that every optimal graph has the form G *1(a,b,c,d) or G *2(a,b,c,d) with b ≤ 1 or c ≤ 1 or d ≤ 1. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 283295, 1999
*Part of this research was conducted while the first author was visiting the University of Rome "La Sapienza" and the Ecole Polytechnique Federale de Lausanne, whose support is gratefully acknowledged.
57 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 2 |
| 2021 | 10 |
| 2020 | 20 |
| 2019 | 14 |
| 2018 | 17 |
| 2017 | 12 |