A Spanning Union of Cycles in Thin Cylinder, Torus and Klein Bottle Grid Graphs

Djokic, Jelena; Doroslovački, Ksenija; Bodroža-Pantić, Olga

doi:10.3390/math11040846

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…In this paper we deal with the former case. In the latter case the coding words are circular and the reader interested in that topic is referred to [8].…”

Section: Introductionmentioning

confidence: 99%

The structure of the 2-factor transfer digraph common for rectangular, thick cylinder and Moebius strip grid graphs

Djokic

Doroslovački

Bodroža-Pantić

2023

APPL ANAL DISCRETE M

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In this paper, we prove that all but one of the components of the transfer digraph D? m needed for the enumeration of 2-factors in the rectangular, thick cylinder and Moebius strip grid graphs of the fixed width m (m ? N) are bipartite digraphs and that their orders could be expressed in term of binomial coefficients. In addition, we prove that the set of vertices of each component consists of all the binary m-words for which the difference of numbers of zeros in odd and even positions is constant.

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“…In this paper we deal with the former case. In the latter case the coding words are circular and the reader interested in that topic is referred to [8].…”

Section: Introductionmentioning

confidence: 99%

The structure of the 2-factor transfer digraph common for rectangular, thick cylinder and Moebius strip grid graphs

Djokic

Doroslovački

Bodroža-Pantić

2023

APPL ANAL DISCRETE M

Self Cite

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The structure of the 2-factor transfer digraph common for thin cylinder, torus and Klein bottle grid graphs

Djokic,

Doroslovacki,

Bodroza-Pantic

2024

Filomat

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We prove that the transfer digraph D* C,m needed for the enumeration of 2-factors in the thin cylinder TnCm(n), torus TGm(n) and Klein bottle KBm(n) (all grid graphs of the fixed width m and with m?n vertices), when m is odd, has only two components of order 2m?1 which are isomorphic. When m is even, D* C,m has [m/2] + 1 components which orders can be expressed via binomial coefficients and all but one of the components are bipartite digraphs. The proof is based on the application of recently obtained results concerning the related transfer digraph for linear grid graphs (rectangular, thick cylinder and Moebius strip).

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Counting Traversing Hamiltonian Cycles in Tiled Graphs

Kalamar

2023

Mathematics

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Recently, the problem of counting Hamiltonian cycles in 2-tiled graphs was resolved by Vegi Kalamar, Bokal, and Žerak. In this paper, we continue our research on generalized tiled graphs. We extend algorithms on counting traversing Hamiltonian cycles from 2-tiled graphs to generalized tiled graphs. We further show that, similarly as for 2-tiled graphs, for a fixed finite set of tiles, counting traversing Hamiltonian cycles can be performed in linear time with respect to the size of such graph, implying that counting traversing Hamiltonian cycles in tiled graphs is fixed-parameter tractable.

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A Spanning Union of Cycles in Thin Cylinder, Torus and Klein Bottle Grid Graphs

Cited by 3 publications

References 17 publications

The structure of the 2-factor transfer digraph common for rectangular, thick cylinder and Moebius strip grid graphs

The structure of the 2-factor transfer digraph common for rectangular, thick cylinder and Moebius strip grid graphs

The structure of the 2-factor transfer digraph common for thin cylinder, torus and Klein bottle grid graphs

Counting Traversing Hamiltonian Cycles in Tiled Graphs

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