Counting Maximal Distance-Independent Sets in Grid Graphs
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 531-557
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Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any 𝓁∈ℕ, maximal distance-𝓁 independent (or simply: maximal 𝓁-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
Keywords:
independent set, grid graph, Fibonacci, Padovan numbers, transfer matrix method
@article{DMGT_2013_33_3_a4,
author = {Euler, Reinhardt and Oleksik, Pawe{\l} and Skupie\'n, Zdzis{\l}aw},
title = {Counting {Maximal} {Distance-Independent} {Sets} in {Grid} {Graphs}},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {531--557},
year = {2013},
volume = {33},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2013_33_3_a4/}
}
TY - JOUR AU - Euler, Reinhardt AU - Oleksik, Paweł AU - Skupień, Zdzisław TI - Counting Maximal Distance-Independent Sets in Grid Graphs JO - Discussiones Mathematicae. Graph Theory PY - 2013 SP - 531 EP - 557 VL - 33 IS - 3 UR - http://geodesic.mathdoc.fr/item/DMGT_2013_33_3_a4/ LA - en ID - DMGT_2013_33_3_a4 ER -
Euler, Reinhardt; Oleksik, Paweł; Skupień, Zdzisław. Counting Maximal Distance-Independent Sets in Grid Graphs. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 3, pp. 531-557. http://geodesic.mathdoc.fr/item/DMGT_2013_33_3_a4/
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