Topic
Boxicity
About: Boxicity is a research topic. Over the lifetime, 139 publications have been published within this topic receiving 1801 citations.
Papers published on a yearly basis
Papers
TL;DR: A weaker but still NP-complete satisfiability problem is introduced to prove NP-completeness of recognizing several classes of intersection graphs of geometric objects in the plane, including grid intersection graphs and graphs of boxicity two.
263 citations
1 Jan 1978
TL;DR: The problem of representing the competition graph as an intersection graph of boxes (k-dimensional rectangles representing ecological niches) in Euclidean k-space is described and the class of graphs which arise as competition graphs of (acyclic) food webs are discussed.
Abstract: Two species in an ecosystem compete if and only if they have intersecting ecological niches Competition can be defined independently by using a food web for the ecosystem, and this notion of competition gives rise to a competition graph This paper briefly describes the problem of representing the competition graph as an intersection graph of boxes (k-dimensional rectangles representing ecological niches) in Euclidean k-space and then discusses the class of graphs which arise as competition graphs of (acyclic) food webs
115 citations
TL;DR: Techniques for computing boxicity are developed, based on the simple observation that b(G)≤k if and only if there is an edge covering of G by spanning subgraphs of G, each of which is a cointerval graph, the complement of an interval graph (a graph of boxicity ≤1.).
93 citations
TL;DR: An axis-parallel b-dimensional box is a Cartesian product R"1xR"2x... xR"b where R"i"i (for 1=1) is the number of rational numbers in the model.
82 citations
Posted Content•
TL;DR: In this article, the concept of treewidth and boxicity was introduced and a simple cycle of length at least b-3 and an induced cycle of at least floor of (log(b-2) to the base Delta + 2, where Delta is its maximum degree.
Abstract: In this paper, we relate the seemingly unrelated concepts of treewidth and boxicity. Our main result is that, for any graph G, boxicity(G) = 3, then there exists a simple cycle of length at least b-3 as well as an induced cycle of length at least floor of (log(b-2) to the base Delta) + 2, where Delta is its maximum degree. We also relate boxicity with the cardinality of minimum vertex cover, minimum feedback vertex cover etc. Another structural consequence is that, for any fixed planar graph H, there is a constant c(H) such that, if boxicity(G) >= c(H) then H is a minor of G.
80 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 6 |
| 2019 | 3 |
| 2018 | 10 |
| 2017 | 3 |
| 2016 | 7 |