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arXiv · 1212.6909

Cycle-continuous mappings -- order structure

Robert Šámal
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Abstract

Given two graphs, a mapping between their edge-sets is cycle-continuous, if the preimage of every cycle is a cycle. The motivation for this notion is Jaeger's conjecture that for every bridgeless graph there is a cycle-continuous mapping to the Petersen graph. Answering a question of DeVos, Nešetřil, and Raspaud, we prove that there exists an infinite set of graphs with no cycle-continuous mapping between them. Further extending this result, we show that every countable poset can be represented by graphs and existence of cycle-continuous mappings between them.

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Robert Šámal. 2012-12-31. Cycle-continuous mappings -- order structure. https://arxiv.org/abs/1212.6909

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