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Monochromatic paths on edge colored digraphs and state splittings

Summary: Monochromatic paths on edge colored
digraphs and state splittings
Hortensia Galeana-S´anchez and Ricardo G´omez
Instituto de Matem´aticas de la Universidad Nacional Aut´onoma de M´exico
Circuito Exterior, Ciudad Universitaria C.P. 04510, M´exico D.F., M´exico
We look at the behavior under state splitting of distinct kinds of
properties regarding monochromatic paths on edge colored digraphs.
These are absorbance and independence as well as the existence of
kernels, semikernels, quasikernels and Grundy functions, all of them
defined in terms of monochromatic paths.
Keywords: absorbance, independence, kernel, semikernel, quasikernel,
Grundy function, monochromatic path, state splitting, duality
MSC: Primary: 05C20; Secondary: 05C69, 05C38
1 Introduction
There has always been interest in studying properties of digraphs under
different kinds of operations (see [1], [6], [9], [14]). Results concerning the
line digraph operator have motivated other kind of operations to be studied.
In [4] the authors look at simple state splitting (a fundamental operation in
symbolic dynamics), and generalize results known for line digraphs. Here we


Source: Aíza, Ricardo Gómez - Instituto de Matemáticas, Universidad Nacional Autónoma de México


Collections: Mathematics