We show that there exist linear-time algorithms that compute the strong chromatic index of Halin graphs, of maximal outerplanar graphs and of distance-hereditary graphs.

A k-dimensional box is the Cartesian product R1 × R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such ...

The Quadratic Travelling Salesman Problem (QTSP) is to find a least cost Hamiltonian cycle in an edge-weighted graph, where costs are defined for all pairs of edges contained in the Hamiltonian cycle. The problem is shown to be strongly NP-hard on a Halin graph. We also consider a variation of the QTSP, called the k-neighbour TSP (TSP(k)). Two edges e and f , e 6= f , are k-neighbours on a tour...

question of Halin, we prove that in a 3-connected graph wit nd the cycle space is generated by induced nonseparating iley Periodicals, Inc. J Graph Theory 00: 1–8, 2003

This paper provides a partial generalization to matroid theory of the result of Halin and Jung that each simple graph with minimum vertex degree at least 4 has K5 or the octahedron K2,2,2 as a minor.