Bipartite graphs of small readability

Rayan Chikhi, Vladan Jovičić, Stefan Kratsch, Paul Medvedev, Martin Milanič, Sofya 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)
Pages (from-to)402-415
Number of pages14
JournalTheoretical Computer Science
Volume806
DOIs
StatePublished - Feb 2 2020

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Chikhi, R., Jovičić, V., Kratsch, S., Medvedev, P., Milanič, M., Raskhodnikova, S., & Varma, N. (2020). Bipartite graphs of small readability. Theoretical Computer Science, 806, 402-415. https://doi.org/10.1016/j.tcs.2019.07.022