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math.CO2024
The Perfect Matching Hamiltonian property in Prism and Crossed Prism graphs
Francesco Colangelo, Federico Romaniello
A graph has the \emph{Perfect Matching Hamiltonian property} (or for short, is ) if, for each one of its perfect matchings, there is another perfect matching of su…
math.CO2024
An updated survey on 2-Factors of Regular Graphs
D. Labbate, F. Romaniello
A 2-factor of a graph is a 2-regular spanning subgraph of . We present a survey summarising results on the structure of 2-factors in regular graphs, as achieved by various r…
math.CO2024★ 1 cited
A sharp upper bound for the harmonious total chromatic number of graphs and multigraphs
M. Abreu, J. B. Gauci, D. Mattiolo +4
A proper total colouring of a graph is called harmonious if it has the further property that when replacing each unordered pair of incident vertices and edges with their colour…