Szczegóły publikacji
Opis bibliograficzny
Factorizations of regular graphs of infinite degree / Marcin STAWISKI // The Electronic Journal of Combinatorics [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 1077-8926 . — 2026 — vol. 33 iss. 1 art. no. P1.23, s. 1–9. — Wymagania systemowe: Adobe Reader. — Bibliogr. s. 9, Abstr. — Publikacja dostępna online od: 2026-02-13
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Dane bibliometryczne
| ID BaDAP | 167617 |
|---|---|
| Data dodania do BaDAP | 2026-05-26 |
| Tekst źródłowy | URL |
| DOI | 10.37236/11536 |
| Rok publikacji | 2026 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | The Electronic Journal of Combinatorics |
Abstract
Let H = (Hi: i < α) for some ordinal number α be an indexed family of graphs. A family G = (Gi: i < α) of edge-disjoint subgraphs of a graph G such that for every i < α: Gi is isomorphic to Hi, each Gi is a spanning subgraph of G, and E(G) =⋃{E(Gi): i < α} is a H-factorization of G. Let κ be an infinite cardinal. Kőnig proved in 1936 that every κ-regular graph has a factorization into perfect matchings. We extend this result to the most general factorizations possible. We study indexed families T = (Ti: i < κ) of graphs without isolated vertices such that every connected κ-regular graph has a T-factorization. We prove that if T is a family of forests each of order at most κ, then every connected κ-regular graph G has a T-factorization. These are the most general assumptions for such a family T for this statement to hold.
