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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F08%3A00500739" target="_blank" >RIV/49777513:23520/08:00500739 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
A note on the dominating circuit conjecture and subgraphs of essentially 4-edge-connected cubic graphs
Original language 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 ?(H)=2 is strongly V2(H)-dominating
Czech name
Poznámka k DCC hypotéze a podgrafům esenciálně souvislých kubických grafů
Czech description
Článek pojednává o souvislosti známé hypotéze o dominantních kružnicích v esenciálně 4-souvislých kubických grafech a podgrafech esenciálně 4-souvislých kubických grafů

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)