2012/12/31 by Robert Šámal, Šámal, Robert
Computer Science · Mathematics · #05C21 #05C38 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C21 #msc:05C38
paper · pdf · doi:10.48550/arxiv.1212.6909
12 pages
arxiv created 2012/12/31 · openalex publication_date 2012/12/31 · arxiv updated 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.