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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)). (en)
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Title
| - High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph
- High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph (en)
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skos:prefLabel
| - High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph
- High-Girth Cubic Graphs are Homomorphic to the Clebsch Graph (en)
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skos:notation
| - RIV/00216208:11320/11:10100998!RIV12-GA0-11320___
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(1M0545), P(GPP201/10/P337), Z(MSM0021620838)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/11:10100998
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Graph; Clebsch; Homomorphic; are; Graphs; Cubic; High-Girth (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Šámal, Robert
- DeVos, Matt
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http://linked.open...ain/vavai/riv/wos
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://bibframe.org/vocab/doi
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http://localhost/t...ganizacniJednotka
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