Cycle-Continuous Mappings-Order Structure

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369126" target="_blank" >RIV/00216208:11320/17:10369126 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/jgt.22047" target="_blank" >http://dx.doi.org/10.1002/jgt.22047</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22047" target="_blank" >10.1002/jgt.22047</a>

Result language
angličtina
Original language name
Cycle-Continuous Mappings-Order Structure
Original language description
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 definition is Jaeger's conjecture that for every bridgeless graph there is a cycle-continuous mapping to the Petersen graph, which, if solved positively, would imply several other important conjectures (e.g., the Cycle double cover conjecture). Answering a question of DeVos, Neetil, 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 the existence of cycle-continuous mappings between them. (C) 2016 Wiley Periodicals, Inc.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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