3 papers
math.CO2025
Degree sequence condition for Hamiltonicity in tough graphs
Songling Shan, Arthur Tanyel
Generalizing both Dirac's condition and Ore's condition for Hamilton cycles, Chvátal in 1972 established a degree sequence condition for the existence of a Hamilton cycle in a gra…
math.CO2025
Hamilton cycles in tough -free graphs
Songling Shan, Arthur Tanyel
In 1973, Chvátal conjectured that there exists a constant such that every -tough graph on at least three vertices is Hamiltonian. While this conjecture is still open, w…
math.CO2025
A strengthening of a degree sequence condition for Hamiltonicity in tough graphs
Songling Shan, Arthur Tanyel
Generalizing Chvátal's classic 1972 result, Hoà ng proposed in 1995 the following conjecture, which strengthens Chvátal's result in terms of toughness: Let be a positive…