Add to ORKGIt has been shown by Carsten Thomassen that when r is suciently large, Lovasz Local Lemma can be applied to show that every Hamiltonian r-regular graph has a second Hamiltonian cycle. The best result obtained by this method is the existence of second Hamiltonian cycles in Hamiltonian r-regular graphs, when r 73. In this note we show that by using Lopsided Local Lemma this can be improved to r 48. We also show that Thomassen's condition for the existence of red-independent green-dominating sets is near optimal
AbstractBill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is ha...
AbstractLet G be a 3-connected, k-regular graph on at most 4k vertices. We show that, for k⩾63, ever...
Given a 2-connected graph G on n vertices, let G* be its partially square graph, obtained by adding ...
AbstractIn 1975, John Sheehan conjectured that every Hamiltonian 4-regular graph has a second Hamilt...
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove ...
Let G be a k-regular 2-connected graph of order n. Jackson proved that G is hamiltonian if n 5 3k. Z...
In 1975, Sheehan conjectured that every simple 4-regular hamiltonian graph has a second Hamilton cyc...
This chapter presents the theorem of Hamiltonian cycles in regular graphs. If in a graph of order n ...
Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four...
AbstractWe give a simpler proof of the theorem due to B. Jackson and Y. Zhu, Z. Liu, and Z. Yu that,...
Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four...
A Hamilton cycle in a graph is a cycle that passes through every vertex of the graph. A graph is cal...
Let G(k) denote the set of connected k-regular graphs G, k ≥ 2, where the number of vertices at dist...
DeLeon 1 A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph ...
In [6], Thomassen conjectured that if I is a set of k \Gamma 1 arcs in a k-strong tournament T , th...
AbstractBill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is ha...
AbstractLet G be a 3-connected, k-regular graph on at most 4k vertices. We show that, for k⩾63, ever...
Given a 2-connected graph G on n vertices, let G* be its partially square graph, obtained by adding ...
AbstractIn 1975, John Sheehan conjectured that every Hamiltonian 4-regular graph has a second Hamilt...
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove ...
Let G be a k-regular 2-connected graph of order n. Jackson proved that G is hamiltonian if n 5 3k. Z...
In 1975, Sheehan conjectured that every simple 4-regular hamiltonian graph has a second Hamilton cyc...
This chapter presents the theorem of Hamiltonian cycles in regular graphs. If in a graph of order n ...
Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four...
AbstractWe give a simpler proof of the theorem due to B. Jackson and Y. Zhu, Z. Liu, and Z. Yu that,...
Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four...
A Hamilton cycle in a graph is a cycle that passes through every vertex of the graph. A graph is cal...
Let G(k) denote the set of connected k-regular graphs G, k ≥ 2, where the number of vertices at dist...
DeLeon 1 A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph ...
In [6], Thomassen conjectured that if I is a set of k \Gamma 1 arcs in a k-strong tournament T , th...
AbstractBill Jackson has proved that every 2-connected, k-regular graph on at most 3k vertices is ha...
AbstractLet G be a 3-connected, k-regular graph on at most 4k vertices. We show that, for k⩾63, ever...
Given a 2-connected graph G on n vertices, let G* be its partially square graph, obtained by adding ...