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Corrigendum to "On the monophonic rank of a graph" [Discrete Math. Theor. Comput. Sci. 24:2 (2022) #3]

Mitre C. Dourado, Vitor S. Ponciano, Rômulo L. O. da Silva

TL;DR

This corrigendum gives a counterexample to Theorem 5.2 in "On the monophonic rank of a graph" and presents a polynomial-time algorithm for computing the monophonic rank of a starlike graph.

Abstract

In this corrigendum, we give a counterexample to Theorem 5.2 in "On the monophonic rank of a graph" [Discrete Math. Theor. Comput. Sci. 24:2 (2022) #3]. We also present a polynomial-time algorithm for computing the monophonic rank of a starlike graph.

Corrigendum to "On the monophonic rank of a graph" [Discrete Math. Theor. Comput. Sci. 24:2 (2022) #3]

TL;DR

This corrigendum gives a counterexample to Theorem 5.2 in "On the monophonic rank of a graph" and presents a polynomial-time algorithm for computing the monophonic rank of a starlike graph.

Abstract

In this corrigendum, we give a counterexample to Theorem 5.2 in "On the monophonic rank of a graph" [Discrete Math. Theor. Comput. Sci. 24:2 (2022) #3]. We also present a polynomial-time algorithm for computing the monophonic rank of a starlike graph.
Paper Structure (2 sections, 4 theorems, 5 equations, 2 figures)

This paper contains 2 sections, 4 theorems, 5 equations, 2 figures.

Table of Contents

  1. The counterexample
  2. Monophonic rank is polynomial for starlike graphs

Key Result

Lemma 1.1

If $G$ is a starlike graph and $S \subseteq V(G)$, then every vertex $v \in \langle S \rangle - S$ belongs to $C'_0$ and is an internal vertex of an induced $(u,u')$-path such that $u \in S \cap Z \cap N(v)$ and $u' \in \langle S \rangle$.

Figures (2)

  • Figure 1: A counterexample to the proof of Theorem $5.2$ in (DPS-2022-mono-rank).
  • Figure 2: Graphs $G_0, G_1$ and $G_3$ constructed from the starlike graph $G$. Ellipses formed by continuous lines represent cliques, while the ones formed by dashed lines represent independent sets.

Theorems & Definitions (8)

  • Lemma 1.1
  • proof
  • Lemma 2.1
  • proof
  • Theorem 2.1
  • proof
  • Corollary 2.1
  • proof