Results 81 to 90 of about 215 (116)
A brief, simple proof of Vizing's conjecture
, 2011 For any graph $G=(V,E)$, a subset $S\subseteq V$ \emph{dominates} $G$ if all vertices are contained in the closed neighborhood of $S$, that is $N[S]=V$. The minimum cardinality over all such $S$ is called the domination number, written $ (G)$. In 1963, V.G.
openaire +2 more sources
Proof of Melnikov-Vizing conjecture for multigraphs with maximum degree at most 3
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
The Berge-F\"uredi conjecture on the chromatic index of hypergraphs with large hyperedges
This paper is concerned with two conjectures which are intimately related. The first is a generalization to hypergraphs of Vizing's Theorem on the chromatic index of a graph and the second is the well-known conjecture of Erd\H{o}s, Faber and Lov\'asz ...
Bretto, Alain +2 more
core
Vizing's conjecture: a survey and recent results
, 2012 Vizingova domneva iz leta 1968 trdi, da je dominacijsko število kartezičnega produkta dveh grafov vsaj tako veliko, kot je produkt dominacijskih števil faktorjev. V članku naredimo pregled različnih pristopov k tej osrednji domnevi iz teorije grafovske dominacije. Ob tem dokažemo tudi nekaj novih rezultatov.
Brešar, Boštjan +6 more
openaire +1 more source
Vizings Conjecture: A Density-Based Re-framing Applied to Bipartite Graphs
We reformulate Vizing's conjecture γ(G\square H) \ge γ(G)γ(H) in terms of normalised domination density and use analytic bounds to delineate regimes where it holds. The conjecture is verified for all bipartite pairs with sufficiently uneven bipartitions.
openaire +2 more sources
Some of the next articles are maybe not open access.
A partition approach to Vizing's conjecture
Journal of Graph Theory, 1996One conjecture of V. G. Vizing says that \(\gamma(G\times H)\geq \gamma(G) \gamma(H)\), where \(\gamma\) is the domination number of a graph. The authors prove the inequalities \(P_2(G)\leq x(G)\leq \gamma(G)\) and \(\gamma(G\times H)\geq x(G) \gamma(H)\). The symbol \(P_2(G)\) denotes the 2-packing number of \(G\), i.e.
Chen, Guantao +2 more
openaire +2 more sources