سیویلیکا را در شبکه های اجتماعی دنبال نمایید.

Login
PapersConferencesJournals

Fundamental Groupoids for Graphs

Publish place: Categories and General Algebraic Structures with Applications، Vol: 16، Issue: 1
Publish Year: 1401
Type: Journal paper
Language: English
View: 199

This Paper With 32 Page And PDF Format Ready To Download

DOWNLOAD Paper

Export:

Link to this Paper:
https://civilica.com/doc/1386967

Document National Code:

JR_CGASAT-16-1_007

Index date: 30 January 2022

Fundamental Groupoids for Graphs abstract

In recent years several notions of discrete homotopy for graphs have been introduced, including a notion of ×-homotopy due to Dochtermann. In this paper, we define a ×-homotopy fundamental groupoid for graphs, and prove that it is a functorial ×-homotopy invariant for finite graphs. We also introduce tools to compute this fundamental groupoid, including a van Kampen theorem. We conclude with a comparison with previous definitions along these lines, including those built on polyhedral complexes of graph morphisms.

Fundamental Groupoids for Graphs Keywords:

Graph , homotopy , groupoid , fundamental group

Fundamental Groupoids for Graphs authors

Tien Chih

Montana State University-Billings

Laura Scull

Fort Lewis College

مراجع و منابع این Paper:

لیست زیر مراجع و منابع استفاده شده در این Paper را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود Paper لینک شده اند :
Babson, E., Barcelo, H., Longueville, M., and Laubenbacher, R., Homotopy ...
Babson, E. and Kozlov, D., Complexes of graph homomorphisms, Isreal ...
Barcelo, H., Kramer, X., Laubenbacher, R. and Weaver, C., Foundations ...
Bonato, A. and Nowakowski, R., “The Game of Cops and ...
Bondy, J. and Murty, U.S.R., “Graph Theory”, Springer, ۲۰۰۸ ...
Brightwell, G. and Winkler, P., Gibbs measures and dismantlable graphs, ...
Brown, R., Groupoids and Van Kampen’s Theorem, Proc. Lond. Math. ...
Bubenik, P. and Milićević, N., Homotopy, homology and persistent homology ...
Chih, T. and Scull, L., A homotopy category for graphs, ...
Chih, T. and Scull, L., Homotopy covers of graphs, https://arxiv.org/abs/۲۰۱۲.۰۵۳۷۸ ...
Dochtermann, A., Hom complexes and homotopy theory in the category ...
Dochtermann, A., Homotopy groups of Hom complexes of graphs, J. ...
Dochtermann, A. and Singh, A., Homomorphism complexes, reconfiguration, and homotopy ...
Fieux, E. and Lacaze, J., Foldings in graphs and relations ...
Grigor’yan, A. and Lin, Y., Muranov, Y., and Yau, S.T., ...
Hardeman, R., The lifting properties of A-homotopy theory, https://arxiv.org/abs/۱۹۰۴.۱۲۰۶۵ ...
Hatcher, A., “Algebraic Topology”, Cambridge University Press, ۲۰۰۱ ...
Hell, P. and Neˇsetˇril, J., “Graphs and homomorphisms”, Oxford University ...
Kozlov, D., Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes, ...
Kozlov, D., Collapsing along monotone poset maps, Int. J. Math. ...
Kozlov, D., Simple homotopy types of Hom-complexes, neighborhood complexes, Lovasz ...
Kozlov, D., A simple proof for folds on both sides ...
Kwak, J.J. and Nedela, R. “Graphs and Their Coverings”, ۲۰۰۵, ...
Lutz, B., Higher discrete homotopy groups of graphs, https://arxiv.org/abs/۲۰۰۳.۰۲۳۹۰[۲۵] Matsushita, ...
Plessas, D., The Categories of Graphs, University of Montana Graduate ...
Riehl, E., “Category Theory in Context”, Dover Publications, ۲۰۱۷ ...
نمایش کامل مراجع