Topic
Petersen graph
About: Petersen graph is a research topic. Over the lifetime, 1493 publications have been published within this topic receiving 22714 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases.
Abstract: It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} . The method is then generalized to obtain upper bounds on the capacity of an arbitrary graph. A well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases. Several results are obtained on the capacity of special graphs; for example, the Petersen graph has capacity four and a self-complementary graph with n points and with a vertex-transitive automorphism group has capacity \sqrt{5} .
1,964 citations
Posted Content•
TL;DR: A heuristic algorithm for finding a graph H as a minor of a graph G that is practical for sparse $G$ and $H$ with hundreds of vertices is presented.
Abstract: We present a heuristic algorithm for finding a graph $H$ as a minor of a graph $G$ that is practical for sparse $G$ and $H$ with hundreds of vertices We also explain the practical importance of finding graph minors in mapping quadratic pseudo-boolean optimization problems onto an adiabatic quantum annealer
395 citations
TL;DR: In this article, it is conjectured that the Petersen graph does not have a Tait coloring, and the conjecture is shown to be equivalent to a combinatorial assertion involving cyclically ordered arrays of n objects each belonging to one of three distinguishable classes.
288 citations
1 Jan 2017
TL;DR: In this article, the authors study how global parameters of a graph, such as its edge density or chromatic number, can influence its local substructures and show that a sufficiently high average degree can ensure that one of these subgraphs occurs.
Abstract: In this chapter we study how global parameters of a graph, such as its edge density or chromatic number, can influence its local substructures. How many edges, for instance, do we have to give a graph on n vertices to be sure that, no matter how these edges are arranged, the graph will contain a K r subgraph for some given r? Or at least a K r minor? Will some sufficiently high average degree or chromatic number ensure that one of these substructures occurs?
283 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 5 |
| 2024 | 5 |
| 2023 | 15 |
| 2022 | 21 |
| 2021 | 25 |
| 2020 | 21 |