Hamiltonian and pseudo-Hamiltonian cycles and fillings in simplicial complexes

نویسندگان

چکیده

We introduce and study a d-dimensional generalization of graph Hamiltonian cycles. These are the cycles in Knd (the complete simplicial d-complex over vertex set size n). d-cycles simple rank, or, equivalently, 1+(n−1d). The discussion is restricted to fields F2 Q. For d=2, we characterize n's for which 2-cycles exist. d=3 it shown that 3-cycles exist infinitely many n's. In general, there always (n−1d)−O(nd−3). All above results constructive. Our approach naturally extends (and fact, involves) d-fillings, generalizing notion T-joins graphs. Given (d−1)-cycle Zd−1∈Knd, F its d-filling if ∂F=Zd−1. call acyclic (n−1d). If d-cycle Z contains d-simplex σ, then Z∖σ ∂σ (a closely related fact also true Q). Thus, two notions related. Most about hold d-fillings as well.

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ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series B

سال: 2021

ISSN: ['0095-8956', '1096-0902']

DOI: https://doi.org/10.1016/j.jctb.2021.04.003