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Topological Graph Theory

Graphs Session #3 #3

Subevent of Graphs Session #3

Central Time (US & Canada)

Starts at: 2025-08-12 03:30PM

Ends at: 2025-08-12 03:55PM

Decomposing 2-cycles of graphs

Hein Van der Holst ⟨hvanderholst@gsu.edu⟩

Abstract:

A 2-cycle on a graph G=(V,E) is a function d:E×EZ such that for each edge e, both d(e,) and d(,e) are circulations on G. For an oriented cycle C and an edge e of G, define C(e)=+1 if C traverses e in forward direction, and C(e)=1 if C traverses e in backward direction. Then examples of 2-cycles are: take two vertex-disjoint oriented cycles C and D of G and define d(e,f)=C(e)D(f). Also on each K3,3- and K5-subdivision are 2-cycles. In this talk, we show that each 2-cycle on G can be written as a sum of four types of special 2-cycles.

This is joint work with Serguei Norine and Robin Thomas.

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