Add to ORKGAbstract It is well known that 3–regular graphs with arbitrarily large girth exist. Three constructions are given that use the former to produce non-Hamiltonian 3–regular graphs without reducing the girth, thereby proving that such graphs with arbitrarily large girth also exist. The resulting graphs can be 1–, 2 – or 3–edge-connected de-pending on the construction chosen. From the constructions arise (naive) upper bounds on the size of the smallest non-Hamiltonian 3–regular graphs with particular girth. Several examples are given of the smallest such graphs for various choices of girth and connectedness
Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hami...
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number ...
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number ...
In 1980, Jackson proved that every 2-connected k-regular graph with at most 3k vertices is Hamiltoni...
In this paper, we explore minimal k-connected non-Hamiltonian graphs. Graphs are said to be minimal ...
AbstractIt is shown that for every value of an integer k, k⩾11, there exist 3-valent 3-connected pla...
We prove that a triangular grid without local cuts is (almost) always Hamiltonian. This suggests an ...
AbstractA known result by the author in 1991 is that every 3-connected claw-free graph on at most 6δ...
A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circum...
AbstractFor certain positive integers k it is shown that there is no k-regular graph with girth 5 ha...
AbstractWe show that all 3-connected cubic planar graphs on 36 or fewer vertices are hamiltonian, th...
We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Pe...
We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Pe...
This chapter presents the theorem of Hamiltonian cycles in regular graphs. If in a graph of order n ...
We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Pe...
Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hami...
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number ...
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number ...
In 1980, Jackson proved that every 2-connected k-regular graph with at most 3k vertices is Hamiltoni...
In this paper, we explore minimal k-connected non-Hamiltonian graphs. Graphs are said to be minimal ...
AbstractIt is shown that for every value of an integer k, k⩾11, there exist 3-valent 3-connected pla...
We prove that a triangular grid without local cuts is (almost) always Hamiltonian. This suggests an ...
AbstractA known result by the author in 1991 is that every 3-connected claw-free graph on at most 6δ...
A graph is called weakly pancyclic if it contains cycles of all lengths between its girth and circum...
AbstractFor certain positive integers k it is shown that there is no k-regular graph with girth 5 ha...
AbstractWe show that all 3-connected cubic planar graphs on 36 or fewer vertices are hamiltonian, th...
We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Pe...
We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Pe...
This chapter presents the theorem of Hamiltonian cycles in regular graphs. If in a graph of order n ...
We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Pe...
Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hami...
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number ...
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number ...