About: A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The well-known dominating circuit conjecture has several interesting reformulations, for example conjectures of Fleischner, Matthews and Sumner, and Thomassen. We present another equivalent version of the dominating circuit conjecture considering subgraphs of essentially 4-edge-connected cubic graphs. Let S={u1,u2,u3,u4} be a set of four distinct vertices of a graph G and V2(G) be a set of all vertices of degree 2 of a graph G. We say that G is S-strongly dominating if the graph arising from G after adding two new edges e1=xy and e2=wz such that {x,y,w,z}=S has a dominating closed trail containing e1 and e2. We show that the dominating circuit conjecture is equivalent to the statement that any subgraph H of an essentially 4-edge-connected cubic graph with V2(H)=4 and minimum degree δ(H)=2 is strongly V2(H)-dominating The well-known dominating circuit conjecture has several interesting reformulations, for example conjectures of Fleischner, Matthews and Sumner, and Thomassen. We present another equivalent version of the dominating circuit conjecture considering subgraphs of essentially 4-edge-connected cubic graphs. Let S={u1,u2,u3,u4} be a set of four distinct vertices of a graph G and V2(G) be a set of all vertices of degree 2 of a graph G. We say that G is S-strongly dominating if the graph arising from G after adding two new edges e1=xy and e2=wz such that {x,y,w,z}=S has a dominating closed trail containing e1 and e2. We show that the dominating circuit conjecture is equivalent to the statement that any subgraph H of an essentially 4-edge-connected cubic graph with V2(H)=4 and minimum degree δ(H)=2 is strongly V2(H)-dominating (en) Článek pojednává o souvislosti známé hypotéze o dominantních kružnicích v esenciálně 4-souvislých kubických grafech a podgrafech esenciálně 4-souvislých kubických grafů (cs)
Title	A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs (en) Poznámka k DCC hypotéze a podgrafům esenciálně souvislých kubických grafů (cs)
skos:prefLabel	A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs (en) Poznámka k DCC hypotéze a podgrafům esenciálně souvislých kubických grafů (cs)
skos:notation	RIV/49777513:23520/08:00500739!RIV09-MSM-23520___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1M0545), Z(MSM4977751301)
http://linked.open...iv/cisloPeriodika	23
http://linked.open...vai/riv/dodaniDat	2009
http://linked.open...aciTvurceVysledku	Kužel, Roman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	354351
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/08:00500739
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	hamiltonian; circuit; cycle; dominating; thomassen; conjecture, cubic; subgraphs (en)
http://linked.open.../riv/klicoveSlovo	cubic circuit conjecture cycle hamiltonian dominating thomassen subgraphs
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[AAEDD350BC27]
http://linked.open...i/riv/nazevZdroje	Discrete Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	308
http://linked.open...iv/tvurceVysledku	Kužel, Roman
http://linked.open...ain/vavai/riv/wos	000260737200047
http://linked.open...n/vavai/riv/zamer	Spojité a diskrétní matematické struktury a vývoj odpovídajících metod jejich zkoumání
issn	0012-365X
number of pages	4 (xsd:int)
http://localhost/t...ganizacniJednotka	23520
is http://linked.open...avai/riv/vysledek of	A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs

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