Abstract
A graph G 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 a 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. Further, using our structural results, we present a polynomial-time algorithm for the Hamiltonian cycle problem and other classical optimization problems such as minimum vertex cover, minimum connected vertex cover, longest cycle, feedback vertex set, treewidth and minimum fill-in.
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