Hamiltonian Spider Intersection Graphs Are Cycle Extendable

A cycle C of length k is extendable if there is a cycle C′ of length k+1 with V (C) ⊂ V (C′). A graph G = (V,E) of order n is cycle extendable when every cycle C of length k < n is extendable. A chordal graph is a spider intersection graph if it admits an intersection representation which consists of subtrees of a sub-divided star (or spider). In 1990, Hendry conjectured that all hamiltonian chordal graphs are cycle extendible, and this conjecture remains unresolved. We show that all hamiltonian spider intersection graphs are cycle extendable, generalizing known results on cycle extendability in interval graphs and split graphs.