2016
DOI: 10.1016/j.dam.2015.07.028
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Some new characterizations of Hamiltonian cycles in triangular grid graphs

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Cited by 13 publications
(16 citation statements)
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“…When we are short of information regarding what "happened" in the later columns, it may just be that some of the windows appear to be disconnected when in reality they are not. The reason for this may lie in the fact that the trees containing them meet at a later column, say, column k. This phenomenon prompted us to introduce the equivalence relation which tells us whether any two windows are "joined at the k-th column," or simply "k-joined" [4,5]. We would like to remark that earlier we had called this relation k-SIST [3], which stands for "surely in the same tree."…”
Section: Rolling Imprints and The K R -Joined Relationmentioning
confidence: 99%
See 1 more Smart Citation
“…When we are short of information regarding what "happened" in the later columns, it may just be that some of the windows appear to be disconnected when in reality they are not. The reason for this may lie in the fact that the trees containing them meet at a later column, say, column k. This phenomenon prompted us to introduce the equivalence relation which tells us whether any two windows are "joined at the k-th column," or simply "k-joined" [4,5]. We would like to remark that earlier we had called this relation k-SIST [3], which stands for "surely in the same tree."…”
Section: Rolling Imprints and The K R -Joined Relationmentioning
confidence: 99%
“…Therefore, it does not come as a surprise to hear that a great many efforts have been put into the enumeration of Hamiltonian paths and cycles for some lattices such as the rectangular grid graphs P m × P n , thin grid cylinder graphs C m × P n+1 and their triangular versions. Some of the papers devoted to this topic make use of coding the vertices of the graphs [2,11,12,13,16], whereas others prefer coding the square or triangular cells of the considered graph [1,3,4,5,15,17,19,20]. Nevertheless, common to almost all of them is the transfer matrix method [6,18] which is also being used here.…”
Section: Introductionmentioning
confidence: 99%
“…Their method was extended to arbitrarily large grids by Bodroža-Pantić et al [14] and by Stoyan and Strehl [15]. Later, Bodroža-Pantić et al gave some explicit generating functions for the number of Hamiltonian cycles in graphs P m P n and C m P n [16,17]. Earlier, Saburo developed a field theoretic approximation of the number of Hamiltonian cycles in graphs C m C n in [18] as well as in planar random lattices [19].…”
Section: Introductionmentioning
confidence: 99%
“…Their method was extended to arbitrarily large grids by Bodroža-Pantić et al [6] and by Stoyan and Strehl [34]. Later, Bodroža-Pantić et al gave some explicit generating functions for the number of Hamiltonian cycles in graphs P m P n and C m P n [4,5]. Earlier, Saburo developed a field theoretic approximation of the number of Hamiltonian cycles in graphs C m C n in [22], as well as in planar random lattices [23].…”
Section: Introductionmentioning
confidence: 99%