# (k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings

Hortensia Galeana-Sánchez; Ricardo Gómez

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 2, page 359-371
- ISSN: 2083-5892

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topHortensia Galeana-Sánchez, and Ricardo Gómez. "(k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings." Discussiones Mathematicae Graph Theory 27.2 (2007): 359-371. <http://eudml.org/doc/270592>.

@article{HortensiaGaleana2007,

abstract = {Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [12]. Properties of line digraphs inherited from the source have been studied, for instance in [7] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel's dual definition) of a digraph and its line digraph coincide. We extend this for (k,l)-kernels in the context of state splittings and also look at (k,l)-semikernels, k-Grundy functions and their duals.},

author = {Hortensia Galeana-Sánchez, Ricardo Gómez},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {state splitting; line digraph; kernel; Grundy function; duality},

language = {eng},

number = {2},

pages = {359-371},

title = {(k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings},

url = {http://eudml.org/doc/270592},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Hortensia Galeana-Sánchez

AU - Ricardo Gómez

TI - (k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 2

SP - 359

EP - 371

AB - Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [12]. Properties of line digraphs inherited from the source have been studied, for instance in [7] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel's dual definition) of a digraph and its line digraph coincide. We extend this for (k,l)-kernels in the context of state splittings and also look at (k,l)-semikernels, k-Grundy functions and their duals.

LA - eng

KW - state splitting; line digraph; kernel; Grundy function; duality

UR - http://eudml.org/doc/270592

ER -

## References

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- [9] M. Kwaśnik, On the (k,l)-kernels, Graph Theory ( agów, 1981), 114-121, Lecture Notes in Math., 1018 (Springer, Berlin, 1983).
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