Arboricity, h-Index, and Dynamic Algorithms

TL;DR

This paper introduces a new data structure for dynamic graph algorithms, improving efficiency for problems like subgraph counting and graph recognition, especially in graphs with low arboricity or h-index.

Contribution

It presents a modified technique based on Chiba and Nishizeki's work, enabling faster algorithms for various graph problems in dynamic settings.

Findings

Improved time complexity for graphs with low arboricity.

Efficient algorithms for recognizing specific graph classes.

Enhanced subgraph counting in dynamic graphs.

Abstract

In this paper we present a modification of a technique by Chiba and Nishizeki [Chiba and Nishizeki: Arboricity and Subgraph Listing Algorithms, SIAM J. Comput. 14(1), pp. 210--223 (1985)]. Based on it, we design a data structure suitable for dynamic graph algorithms. We employ the data structure to formulate new algorithms for several problems, including counting subgraphs of four vertices, recognition of diamond-free graphs, cop-win graphs and strongly chordal graphs, among others. We improve the time complexity for graphs with low arboricity or h-index.