This HTML5 document contains 49 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
n12http://localhost/temp/predkladatel/
n16http://linked.opendata.cz/resource/domain/vavai/projekt/
n11http://linked.opendata.cz/resource/domain/vavai/riv/tvurce/
n22http://linked.opendata.cz/resource/domain/vavai/subjekt/
n21http://linked.opendata.cz/ontology/domain/vavai/
n8http://linked.opendata.cz/resource/domain/vavai/zamer/
shttp://schema.org/
skoshttp://www.w3.org/2004/02/skos/core#
rdfshttp://www.w3.org/2000/01/rdf-schema#
n3http://linked.opendata.cz/ontology/domain/vavai/riv/
n14http://bibframe.org/vocab/
n2http://linked.opendata.cz/resource/domain/vavai/vysledek/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
n6http://linked.opendata.cz/resource/domain/vavai/vysledek/RIV%2F00216208%3A11320%2F11%3A10100998%21RIV12-GA0-11320___/
n5http://linked.opendata.cz/ontology/domain/vavai/riv/klicoveSlovo/
n10http://linked.opendata.cz/ontology/domain/vavai/riv/duvernostUdaju/
xsdhhttp://www.w3.org/2001/XMLSchema#
n19http://linked.opendata.cz/ontology/domain/vavai/riv/jazykVysledku/
n15http://linked.opendata.cz/ontology/domain/vavai/riv/aktivita/
n20http://linked.opendata.cz/ontology/domain/vavai/riv/druhVysledku/
n13http://linked.opendata.cz/ontology/domain/vavai/riv/obor/
n4http://reference.data.gov.uk/id/gregorian-year/

Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F11%3A10100998%21RIV12-GA0-11320___
rdf:type
skos:Concept n21:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1002/jgt.20580
dcterms:description
We give a (computer assisted) proof that the edges of every graph with maximum degree 3 and girth at least 17 may be 5-colored (possibly improperly) so that the complement of each color class is bipartite. Equivalently, every such graph admits a homomorphism to the Clebsch graph (Fig. 1). Hopkins and Staton [J Graph Theory 6(2) (1982), 115-121] and Bondy and Locke [J Graph Theory 10(4) (1986), 477-504] proved that every (sub)cubic graph of girth at least 4/5 has an edge-cut containing at least of the edges. The existence of such an edge-cut follows immediately from the existence of a 5-edge-coloring as described above; so our theorem may be viewed as a coloring extension of their result (under a stronger girth assumption). Every graph which has a homomorphism to a cycle of length five has an above-described 5-edge-coloring; hence our theorem may also be viewed as a weak version of Nesetril''s Pentagon Problem (which asks whether every cubic graph of sufficiently high girth is homomorphic to C(5)). We give a (computer assisted) proof that the edges of every graph with maximum degree 3 and girth at least 17 may be 5-colored (possibly improperly) so that the complement of each color class is bipartite. Equivalently, every such graph admits a homomorphism to the Clebsch graph (Fig. 1). Hopkins and Staton [J Graph Theory 6(2) (1982), 115-121] and Bondy and Locke [J Graph Theory 10(4) (1986), 477-504] proved that every (sub)cubic graph of girth at least 4/5 has an edge-cut containing at least of the edges. The existence of such an edge-cut follows immediately from the existence of a 5-edge-coloring as described above; so our theorem may be viewed as a coloring extension of their result (under a stronger girth assumption). Every graph which has a homomorphism to a cycle of length five has an above-described 5-edge-coloring; hence our theorem may also be viewed as a weak version of Nesetril''s Pentagon Problem (which asks whether every cubic graph of sufficiently high girth is homomorphic to C(5)).
dcterms:title
High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph
skos:prefLabel
High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph
skos:notation
RIV/00216208:11320/11:10100998!RIV12-GA0-11320___
n21:predkladatel
n22:orjk%3A11320
n3:aktivita
n15:Z n15:P
n3:aktivity
P(1M0545), P(GPP201/10/P337), Z(MSM0021620838)
n3:cisloPeriodika
3
n3:dodaniDat
n4:2012
n3:domaciTvurceVysledku
n11:8865574
n3:druhVysledku
n20:J
n3:duvernostUdaju
n10:S
n3:entitaPredkladatele
n6:predkladatel
n3:idSjednocenehoVysledku
202067
n3:idVysledku
RIV/00216208:11320/11:10100998
n3:jazykVysledku
n19:eng
n3:klicovaSlova
Graph; Clebsch; Homomorphic; are; Graphs; Cubic; High-Girth
n3:klicoveSlovo
n5:High-Girth n5:Clebsch n5:Cubic n5:Graph n5:are n5:Graphs n5:Homomorphic
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[7A1F33851113]
n3:nazevZdroje
Journal of Graph Theory
n3:obor
n13:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n16:GPP201%2F10%2FP337 n16:1M0545
n3:rokUplatneniVysledku
n4:2011
n3:svazekPeriodika
66
n3:tvurceVysledku
DeVos, Matt Šámal, Robert
n3:wos
000287676100005
n3:zamer
n8:MSM0021620838
s:issn
0364-9024
s:numberOfPages
19
n14:doi
10.1002/jgt.20580
n12:organizacniJednotka
11320