Niels Grüttemeier ; Christian Komusiewicz ; Jannik Schestag ; Frank Sommer - Destroying Bicolored $P_3$s by Deleting Few Edges

dmtcs:6108 - Discrete Mathematics & Theoretical Computer Science, June 8, 2021, vol. 23 no. 1 -
Destroying Bicolored $P_3$s by Deleting Few EdgesArticle

Authors: Niels Grüttemeier ; Christian Komusiewicz ORCID; Jannik Schestag ; Frank Sommer ORCID

    We introduce and study the Bicolored $P_3$ Deletion problem defined as follows. The input is a graph $G=(V,E)$ where the edge set $E$ is partitioned into a set $E_r$ of red edges and a set $E_b$ of blue edges. The question is whether we can delete at most $k$ edges such that $G$ does not contain a bicolored $P_3$ as an induced subgraph. Here, a bicolored $P_3$ is a path on three vertices with one blue and one red edge. We show that Bicolored $P_3$ Deletion is NP-hard and cannot be solved in $2^{o(|V|+|E|)}$ time on bounded-degree graphs if the ETH is true. Then, we show that Bicolored $P_3$ Deletion is polynomial-time solvable when $G$ does not contain a bicolored $K_3$, that is, a triangle with edges of both colors. Moreover, we provide a polynomial-time algorithm for the case that $G$ contains no blue $P_3$, red $P_3$, blue $K_3$, and red $K_3$. Finally, we show that Bicolored $P_3$ Deletion can be solved in $ O(1.84^k\cdot |V| \cdot |E|)$ time and that it admits a kernel with $ O(k\Delta\min(k,\Delta))$ vertices, where $\Delta$ is the maximum degree of $G$.

    Volume: vol. 23 no. 1
    Section: Graph Theory
    Published on: June 8, 2021
    Accepted on: May 7, 2021
    Submitted on: February 17, 2020
    Keywords: Computer Science - Data Structures and Algorithms,Computer Science - Discrete Mathematics,Mathematics - Combinatorics

    Consultation statistics

    This page has been seen 585 times.
    This article's PDF has been downloaded 243 times.