Affiliation:
1. Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, India
Abstract
A graph [Formula: see text] is a 3-degree 4-chordal graph if every cycle of length at least five has a chord and the degree of each vertex is at most three. In this paper, we investigate the structure of 3-degree 4-chordal graphs, which is a subclass of 3-degree graphs. We present a structural characterization based on minimal vertex separators and bi-connected components. Many classical problems are known to be NP-complete for 3-degree graphs, and 3-degree 4-chordal graphs are a nontrivial subclass of 3-degree graphs. Using our structural results, we present polynomial-time algorithms for many classical problems which are grouped into (i) subset problems (vertex cover and its variants, feedback vertex set, Steiner tree), (ii) Hamiltonicity and its variants, (iii) graph embedding problems (treewidth, minimum fill-in), and (iv) Coloring problems(rainbow coloring).
Funder
National Board for Higher Mathematics
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics