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(Lack of) model structures on the category of graphs

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Publication:2046255
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DOI10.1007/s10485-021-09630-4zbMath1471.05026arXiv1902.09182OpenAlexW3134518383MaRDI QIDQ2046255

Shuchita Goyal, Rekha Santhanam

Publication date: 17 August 2021

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.09182


zbMATH Keywords

model structures\(\times\)-homotopy equivalencescategory of finite graphs


Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Homotopy theory (55P99) Coloring of graphs and hypergraphs (05C15) Categories of fibrations, relations to (K)-theory, relations to type theory (18N45)


Related Items

Nonexistence of colimits in naive discrete homotopy theory ⋮ Homomorphism complexes, reconfiguration, and homotopy for directed graphs



Cites Work

  • Unnamed Item
  • Homotopy theory of cofibration categories
  • Hom complexes and homotopy theory in the category of graphs
  • Finding paths between graph colourings: PSPACE-completeness and superpolynomial distances
  • Box complexes and homotopy theory of graphs
  • Quillen model structures on the category of graphs
  • The homotopy category is a homotopy category
  • Introduction to homotopy theory
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