Prossimo Seminario

12 Dicembre 2025

ore 14:30, Aula 2

Marién Abreu

(Univ. della Basilicata)

Factors and Hamiltonicity in regular graphs

Abstract: Graphs in which al vertices have the same degree r are called r-regular. If r=3 the graph is said to be cubic. The study of cubic graphs is very vast mainly because some important conjectures in graph theory such as the cycle double cover and Berge-Fulkerson conjectures will be true if proven for cubic graphs.

An r-regular spanning subgraph of a graph is called an r-factor. Several kinds of problems that arise when studying 2-factors of regular graphs will be presented here. In particular, 2-factor hamiltonian, 2-factor isomorphic, pseudo 2-factor isomorphic graphs will be considered. These are respectively graphs in which all 2-factors are hamiltonian, all 2-factors are isomorphic (collection of cycles of same lengths), all $2$-factors have the same parity of number of cycles.

Partial solutions and infinite families with prescribed characteristics will be illustrated, sometimes in the special case of cubic graphs, together with old and new results.

Also the problem of extending a 1-factor to a Hamiltonian cycle in a graph will be considered and results will be presented for several families of graphs including line graphs and cartesian products of graphs and, in particular, prism graphs.

Calendario Generale:

In rosso i seminari futuri.

• 16 Dicembre 2025, G. Rosso (Concordia Un.), A non-archimedean Ax–Lindemann theorem for Shimura varieties.

• 12 Dicembre 2025, M. Abreu (Un. Basilicata), Factors and Hamiltonicity in regular graphs

• 29 Ottobre 2025, M. Mula (Bundeswehr Un.), Modular polynomials for cryptography: zero-knowledge from genus-zero modular curves

• 19 Giugno 2025, C. Sava (Charles Un.),  ∞-Dold-Kan correspondence via representation theory

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• 25 Marzo 2025, M. Rossi (Milano Bicocca), Some results on the geometry of arithmetic random waves

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• 28 Febbraio 2025, F.M. Saettone (Weizmann Inst. Sc.), Equidistribution of CM points via Drinfeld uniformization and automorphic forms

• 20 Febbraio 2025, M. Longo (Padova), On the Tamagawa number conjecture for motives of modular forms

• 29 Gennaio 2025, D. Spriano (Oxford), No finitely generated group is indigestible for the Loch-Ness monster.

• 16 Gennaio 2025, A. Conti (Heidelberg), Bogomolov property for Galois representations with big local image.

• 13 Novembre 2024; F. Cioffi (Napoli), Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases on Hilbert schemes.

• [Mathlab] 30 Ottobre 2024, Y. Bugeaud (Strasbourg), On the decimal expansion of e.

• 1 Ottobre 2024, L. De Feo (IBM Zürich), The isogeny toolbox

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• 11 Aprile 2024, M. Gran (Louvain-la-neuve), On the naturalness of Mal'tsev categories

• 15 Marzo 2024, J. Jenvrin (Grenoble), On the height of some generators of Galois extensions with big Galois groups