Bipartite graphs of small readability

R. Chikhi, Vladan Jovičić, Stefan Kratsch, Paul Medvedev, Martin Milanič, S. Raskhodnikova, Nithin Varma

Research output: Contribution to journalArticle

Abstract

We study a parameter of bipartite graphs called readability, introduced by Chikhi et al. (Discrete Applied Mathematics, 2016) and motivated by applications of overlap graphs in bioinformatics. The behavior of the parameter is poorly understood. The complexity of computing it is open and it is not known whether the decision version of the problem is in NP. The only known upper bound on the readability of a bipartite graph (following from a work of Braga and Meidanis, LATIN 2002) is exponential in the maximum degree of the graph. Graphs that arise in bioinformatics applications have low readability. In this paper, we focus on graph families with readability o(n), where n is the number of vertices. We show that the readability of n-vertex bipartite chain graphs is between Ω(log⁡n) and O(n). We give an efficiently testable characterization of bipartite graphs of readability at most 2 and completely determine the readability of grids, showing in particular that their readability never exceeds 3. As a consequence, we obtain a polynomial time algorithm to determine the readability of induced subgraphs of grids. One of the highlights of our techniques is the appearance of Euler's totient function in the analysis of the readability of bipartite chain graphs. We also develop a new technique for proving lower bounds on readability, which is applicable to dense graphs with a large number of distinct degrees.

Original languageEnglish (US)
JournalTheoretical Computer Science
DOIs
StatePublished - Jan 1 2019

Fingerprint

Bioinformatics
Bipartite Graph
Chain Graph
Graph in graph theory
Polynomials
Euler's phi function
Grid
Euler Function
Discrete mathematics
Induced Subgraph
Applied mathematics
Maximum Degree
Polynomial-time Algorithm
Overlap
Exceed
Lower bound
Upper bound
Distinct
Computing
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Chikhi, R., Jovičić, V., Kratsch, S., Medvedev, P., Milanič, M., Raskhodnikova, S., & Varma, N. (2019). Bipartite graphs of small readability. Theoretical Computer Science. https://doi.org/10.1016/j.tcs.2019.07.022
Chikhi, R. ; Jovičić, Vladan ; Kratsch, Stefan ; Medvedev, Paul ; Milanič, Martin ; Raskhodnikova, S. ; Varma, Nithin. / Bipartite graphs of small readability. In: Theoretical Computer Science. 2019.
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Chikhi, R, Jovičić, V, Kratsch, S, Medvedev, P, Milanič, M, Raskhodnikova, S & Varma, N 2019, 'Bipartite graphs of small readability', Theoretical Computer Science. https://doi.org/10.1016/j.tcs.2019.07.022

Bipartite graphs of small readability. / Chikhi, R.; Jovičić, Vladan; Kratsch, Stefan; Medvedev, Paul; Milanič, Martin; Raskhodnikova, S.; Varma, Nithin.

In: Theoretical Computer Science, 01.01.2019.

Research output: Contribution to journalArticle

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Chikhi R, Jovičić V, Kratsch S, Medvedev P, Milanič M, Raskhodnikova S et al. Bipartite graphs of small readability. Theoretical Computer Science. 2019 Jan 1. https://doi.org/10.1016/j.tcs.2019.07.022