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- W3202350488 abstract "Motivated to find the answers to some of the questions that have occurred in recent papers dealing with Hamiltonian cycles (abbreviated HCs) in some special classes of grid graphs we started the investigation of spanning unions of cycles, the so-called 2-factors, in these graphs (as a generalizations of HCs). For all the three types of graphs from the title and for any integer $m geq 2$ we propose an algorithm for obtaining a specially designed digraph ${cal D}^*_m$. The problem of enumeration of 2-factors is reduced to the problem of enumerating oriented walks in this digraph. Computational results we gathered for $m leq 17$ reveal some interesting properties both for the digraphs ${cal D}^*_m$ and for the sequences of numbers of 2-factors. We prove some of them for arbitrary $m geq 2$." @default.
- W3202350488 created "2021-10-11" @default.
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- W3202350488 date "2021-09-25" @default.
- W3202350488 modified "2023-09-27" @default.
- W3202350488 title "Spanning union of cycles in some specific grid graphs with square cells -- PART I: Rectangular Grid Graph $RG_{m}(n)$, Thick Grid Cylinder $TkC_m(n)$ and Moebius Strip $MS_{m}(n)$" @default.
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