Non-hamiltonian bicubic graphs

Non-Isomorphic Smallest Maximally Non-Hamiltonian Graphs

A graph G is maximally non-hamiltonian (MNH) if G is not hamiltonian but becomes hamiltonian after adding an arbitrary new edge. Bondy 2] showed that the smallest size (= number of edges) in a MNH graph of order n is at least d 3n 2 e for n 7. The fact that equality may hold there for innnitely many n was suggested by Bollobbs 1]. This was connrmed by Clark, Entringer and Shapiro (see 5, 6]) an...

Better Approximations of Non-Hamiltonian Graphs

Although there have been a lot of efforts to seek nice characterization of non-Hamiltonian graphs, little progress has been made so far. An important progress was achieved by Chvital [5, 61 who introduced the class of non-l-tough graphs (Nl T) and the class of non-sub-2-factor graphs (NS2F). Both contain only non-Hamiltonian graphs and the conditions for membership can be checked in non-determi...

A large set of non-Hamiltonian graphs

Maximally non-hamiltonian graphs of girth 7

We describe a sufficient condition for graphs used in a construction of Thomassen (which yields hypohamiltonian graphs) to produce maximally non-hamiltonian (MNH) graphs as well. Then we show that the Coxeter graph fulfils this sufficient condition, and thus applying the Thomassen’s construction to multiple copies of the Coxeter graph yields infinitely many MNH graphs with girth 7. So far, the ...

Non-Hamiltonian Holes in Grid Graphs

In this paper we extend general grid graphs to the grid graphs consist of polygons tiling on a plane, named polygonal grid graphs. With a cycle basis satisfied polygons tiling, we study the cyclic structure of Hamilton graphs. A Hamilton cycle can be expressed as a symmetric difference of a subset of cycles in the basis. From the combinatorial relations of vertices in the subset of cycles in th...