Fundamental groupoids of digraphs and graphs
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We introduce the notion of fundamental groupoid of a digraph and prove its basic properties. In particular, we obtain a product theorem and an analogue of the Van Kampen theorem. Considering the category of (undirected) graphs as the full subcategory of digraphs, we transfer the results to the category of graphs. As a corollary we obtain the corresponding results for the fundamental groups of digraphs and graphs. We give an application to graph coloring.
Keywordsdigraph fundamental group fundamental groupoid product of graphs
MSC 201005C25 05C38 05C76 20L05 57M15
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- P. Hell, J. Nešetřil: Graphs and Homomorphisms. Oxford Lecture Series in Mathematics and Its Applications 28, Oxford University Press, Oxford, 2004.Google Scholar