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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 1, Pages 14–20 (Mi ivm6549)  
This article is cited in 2 scientific papers (total in 2 papers)

A vector space approach to the road coloring problem

G. Budzban, Ph. Feinsilver

Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, IL, USA
Full-text PDF (178 kB) Citations (2)
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Abstract: Let $G$ be a strongly connected, aperiodic, two-out digraph with adjacency matrix $A$. Suppose $A=R+B$ are coloring matrices: that is, matrices that represent the functions induced by an edge-coloring of $G$. We introduce a matrix $\Delta=\frac12(R-B)$ and investigate its properties. A number of useful conditions involving $\Delta$ which either are equivalent to or imply a solution to the road coloring problem are derived.
Keywords: digraph, synchronizing automaton, road coloring.
Received: 21.10.2006
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 1, Pages 10–15
DOI: https://doi.org/10.3103/S1066369X10010020
Bibliographic databases:
UDC: 519.713
Language: Russian
Citation: G. Budzban, Ph. Feinsilver, “A vector space approach to the road coloring problem”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 1, 14–20; Russian Math. (Iz. VUZ), 54:1 (2010), 10–15
Citation in format AMSBIB
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\by G.~Budzban, Ph.~Feinsilver
\paper A vector space approach to the road coloring problem
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 1
\pages 14--20
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2664482}
\zmath{https://zbmath.org/?q=an:05666476}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 1
\pages 10--15
\crossref{https://doi.org/10.3103/S1066369X10010020}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649583447}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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