2018/09/24 by Amin Bahmanian, Bahmanian, Amin, Mateja Šajna +1
Computer Science · Engineering · #05B30 #05C38 #05C51 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Interconnection Networks and Systems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1809.09305
openalex publication_date 2018/09/24 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
We construct new resolvable decompositions of complete multigraphs and\ncomplete equipartite multigraphs into cycles of variable lengths (and a perfect\nmatching if the vertex degrees are odd). We develop two techniques: em\nlayering, which allows us to obtain 2-factorizations of complete multigraphs\nfrom existing 2-factorizations of complete graphs, and em detachment, which\nallows us to construct resolvable cycle decompositions of complete equipartite\nmultigraphs from existing resolvable cycle decompositions of complete\nmultigraphs. These techniques are applied to obtain new 2-factorizations of a\nspecified type for both complete multigraphs and complete equipartite\nmultigraphs, with the emphasis on new solutions to the Oberwolfach Problem and\nthe Hamilton-Waterloo Problem. In addition, we show existence of some\n\α-resolvable cycle decompositions.\n