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Fundamental groupoids of digraphs and graphs

Alexander Grigor'yan; Rolando Jimenez; Yuri Muranov

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 1, page 35-65
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Grigor'yan, Alexander, Jimenez, Rolando, and Muranov, Yuri. "Fundamental groupoids of digraphs and graphs." Czechoslovak Mathematical Journal 68.1 (2018): 35-65. <http://eudml.org/doc/294469>.

@article{Grigoryan2018,
abstract = {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.},
author = {Grigor'yan, Alexander, Jimenez, Rolando, Muranov, Yuri},
journal = {Czechoslovak Mathematical Journal},
keywords = {digraph; fundamental group; fundamental groupoid; product of graphs},
language = {eng},
number = {1},
pages = {35-65},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Fundamental groupoids of digraphs and graphs},
url = {http://eudml.org/doc/294469},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Grigor'yan, Alexander
AU - Jimenez, Rolando
AU - Muranov, Yuri
TI - Fundamental groupoids of digraphs and graphs
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 35
EP - 65
AB - 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.
LA - eng
KW - digraph; fundamental group; fundamental groupoid; product of graphs
UR - http://eudml.org/doc/294469
ER -

References

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  8. Grigor'yan, A., Lin, Y., Muranov, Y., Yau, S.-T., 10.4310/PAMQ.2014.v10.n4.a2, Pure Appl. Math. Q. 10 (2014), 619-674. (2014) Zbl1312.05063MR3324763DOI10.4310/PAMQ.2014.v10.n4.a2
  9. Grigor'yan, A., Lin, Y., Muranov, Y., Yau, S.-T., 10.4310/AJM.2015.v19.n5.a5, Asian J. Math. 19 (2015), 887-931. (2015) Zbl1329.05132MR3431683DOI10.4310/AJM.2015.v19.n5.a5
  10. Grigor'yan, A., Muranov, Y. V., Yau, S.-T., 10.4310/HHA.2014.v16.n1.a16, Homology Homotopy Appl. 16 (2014), 295-311. (2014) Zbl1297.05269MR3211747DOI10.4310/HHA.2014.v16.n1.a16
  11. Hatcher, A., Algebraic Topology, Cambridge University Press, Cambridge (2002). (2002) Zbl1044.55001MR1867354
  12. Hell, P., Nešetřil, J., 10.1093/acprof:oso/9780198528173.001.0001, Oxford Lecture Series in Mathematics and Its Applications 28, Oxford University Press, Oxford (2004). (2004) Zbl1062.05139MR2089014DOI10.1093/acprof:oso/9780198528173.001.0001
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