Bipartite (P_6,C_6 )-Free Graphs, Recognition and Optimization Problems

Ruzayn Quaddoura; Ahmad Al-qerem

doi:10.20944/preprints202402.1561.v1

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preprints.org > computer science and mathematics > discrete mathematics and combinatorics > doi: 10.20944/preprints202402.1561.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Bipartite (P_6,C_6 )-Free Graphs, Recognition and Optimization Problems

Ruzayn Quaddoura

^* and

Ahmad Al-qerem

Version 1 : Received: 26 February 2024 / Approved: 27 February 2024 / Online: 27 February 2024 (15:57:01 CET)

A peer-reviewed article of this Preprint also exists.

Quaddoura, R.; Al-qerem, A. Bipartite (P₆, C₆)-Free Graphs: Recognition and Optimization Problems. Symmetry 2024, 16, 447. Quaddoura, R.; Al-qerem, A. Bipartite (P6, C6)-Free Graphs: Recognition and Optimization Problems. Symmetry 2024, 16, 447.

Abstract

The canonical decomposition of a bipartite graph is a new decompositionmethod that involves three operators, parallel, series and K+S. The class of weak bisblit graphs is totally decomposable with respect of these operators, and the class of bicographs is totally decomposable with respect of parallel and series operators. We prove in this paper that the class of bipartite (P_6,C_6)-free graphs is exactly the class of bipartite graphs that are totally decomposable with respect of parallel and K+S operators. We simplify the recognition algorithm of weak-bisplit graphs to adepte with bipartite (P_6,C_6)-free graphs. As a result of this adapted algorithm, we prsent efficient solutions in this class of graphs for two optimization graph problems, the first is the maximm balanced bi-clique problem and the the second is the maximum independent set problem.

Keywords

Bipartite graphs; Graphs Decomposition; Complexity; Optimization Problems

Subject

Computer Science and Mathematics, Discrete Mathematics and Combinatorics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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