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http://hdl.handle.net/2080/3340
Title: | Equidistant Paths in Graphs |
Authors: | Balachandran, Niranjan P, Sajith Mishra, Tapas Kumar L, Sunil Chandran |
Keywords: | Graph G Disjoint paths |
Issue Date: | Jun-2019 |
Citation: | Research Initiation Workshop, IISc Bangalore,10-16 June 2019. |
Abstract: | Let n and k be integers, n ≥ k ≥ 1. A graph G is said to admit property Pk if for any distinct pair x, y ∈ V (G), there exists k internally vertex disjoint paths between x and y of the same length. Consider the following family of graphs. G n k := {Gn : Gn admits property Pk}. There are two interesting directions in the study of G n k . Firstly, in the extremal direction, it is interesting to estimate the sparsity of graphs admitting property Pk. That is, estimation of ν(n, k) = min{|E(Gn)| : Gn ∈ Gn k }. The other direction is structural: what properties in the graph ensures admittance of property Pk. In this paper, we tackle the extremal question followed by some structural results on the same. |
Description: | Copyright of this document belongs to proceedings publisher. |
URI: | http://hdl.handle.net/2080/3340 |
Appears in Collections: | Conference Papers |
Files in This Item:
File | Description | Size | Format | |
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2019_RIW_TKMishra_Equidistant.pdf | Conference Paper | 184.46 kB | Adobe PDF | View/Open |
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