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Lettericity of graphs: an FPT algorithm and a bound on the size of obstructions

2024/02/19 by Bogdan Alecu, Alecu, Bogdan, Mamadou Moustapha Kanté +5
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2402.12559

openalex publication_date 2024/02/19 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28

Abstract

Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property implies that any hereditary class of graphs of bounded lettericity can be described by finitely many forbidden induced subgraphs. This, in turn, implies, in a non-constructive way, polynomial-time recognition of such classes. However, no constructive algorithms and no specific bounds on the size of forbidden graphs are available up to date. In the present paper, we develop an algorithm that recognizes n-vertex graphs of lettericity at most k in time f(k)n3 and show that any minimal graph of lettericity more than k has at most 2O(k2log k) vertices.

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