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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10126092%21RIV13-MSM-11320___
rdf:type
skos:Concept n8:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1016/j.ejc.2011.11.005
dcterms:description
We consider mappings between edge sets of graphs that lift tensions to tensions. Such mappings are called tension-continuous mappings (shortly TT mappings). The existence of a TT mapping induces a (quasi)order on the class of graphs, which seems to be an essential extension of the homomorphism order (studied extensively, see Hell and Nešetřil (2004) [10]). In this paper we study the relationship of the homomorphism and TT orders. We stress the similarities and the differences in both deterministic and random settings. Particularly, we prove that TT order is universal and investigate graphs for which homomorphisms and TT mappings coincide (so-called homotens graphs). In the course of our study, we prove a new Ramsey-type theorem, which may be of independent interest. We solve a problem asked in [Matt DeVos, Jaroslav Nešetřil, André Raspaud, On edge-maps whose inverse preserves flows and tensions, in: J.A. Bondy, J. Fonlupt, J.-L. Fouquet, J.-C. Fournier, J.L. Ramirez Alfonsin (Eds.), Graph Theory in Paris: Proceedings of a Conference in Memory of Claude Berge, in: Trends in Mathematics, Birkhauser, 2006]. We consider mappings between edge sets of graphs that lift tensions to tensions. Such mappings are called tension-continuous mappings (shortly TT mappings). The existence of a TT mapping induces a (quasi)order on the class of graphs, which seems to be an essential extension of the homomorphism order (studied extensively, see Hell and Nešetřil (2004) [10]). In this paper we study the relationship of the homomorphism and TT orders. We stress the similarities and the differences in both deterministic and random settings. Particularly, we prove that TT order is universal and investigate graphs for which homomorphisms and TT mappings coincide (so-called homotens graphs). In the course of our study, we prove a new Ramsey-type theorem, which may be of independent interest. We solve a problem asked in [Matt DeVos, Jaroslav Nešetřil, André Raspaud, On edge-maps whose inverse preserves flows and tensions, in: J.A. Bondy, J. Fonlupt, J.-L. Fouquet, J.-C. Fournier, J.L. Ramirez Alfonsin (Eds.), Graph Theory in Paris: Proceedings of a Conference in Memory of Claude Berge, in: Trends in Mathematics, Birkhauser, 2006].
dcterms:title
Tension continuous maps-Their structure and applications Tension continuous maps-Their structure and applications
skos:prefLabel
Tension continuous maps-Their structure and applications Tension continuous maps-Their structure and applications
skos:notation
RIV/00216208:11320/12:10126092!RIV13-MSM-11320___
n8:predkladatel
n9:orjk%3A11320
n3:aktivita
n20:P
n3:aktivity
P(1M0545)
n3:cisloPeriodika
6
n3:dodaniDat
n15:2013
n3:domaciTvurceVysledku
n7:8865574 n7:1111116
n3:druhVysledku
n21:J
n3:duvernostUdaju
n5:S
n3:entitaPredkladatele
n4:predkladatel
n3:idSjednocenehoVysledku
173759
n3:idVysledku
RIV/00216208:11320/12:10126092
n3:jazykVysledku
n17:eng
n3:klicovaSlova
Tension continuous maps
n3:klicoveSlovo
n10:Tension%20continuous%20maps
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[6C2B72C2A447]
n3:nazevZdroje
European Journal of Combinatorics
n3:obor
n19:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n6:1M0545
n3:rokUplatneniVysledku
n15:2012
n3:svazekPeriodika
33
n3:tvurceVysledku
Nešetřil, Jaroslav Šámal, Robert
s:issn
0195-6698
s:numberOfPages
19
n16:doi
10.1016/j.ejc.2011.11.005
n13:organizacniJednotka
11320