Results 71 to 80 of about 113,121 (99)

Kimmerle conjecture for the Held and O'Nan sporadic simple groups [PDF]

, 2009
Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups.
Bódi, Viktor, Grishkov, A. N., Konovalov, A. B.   +2 more
core   +1 more source

Vizing's conjecture for cographs

, 2016
We show that if $G$ is a cograph, that is $P_4$-free, then for any graph $H$, $γ(G\square H)\geq γ(G)γ(H)$. By the characterization of cographs as a finite sequence of unions and joins of $K_1$, this result easily follows from that of Bartsalkin and German. However, the techniques used are new and may be useful to prove other results.
openaire   +2 more sources

Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture

, 2012
Features recent advances and new applications in graph edge coloring Reviewing recent advances in the Edge Coloring Problem, Graph Edge Coloring: Vizing's Theorem and Goldberg's Conjecture provides an overview of the current state of the science ...
Scheide, Diego, Stiebitz, Michael, Favrholdt, Lene M, Toft, Bjarne   +3 more
core  

Vizing's 2-Factor Conjecture Involving Toughness and Maximum Degree Conditions

The Electronic Journal of Combinatorics, 2019
Let $G$ be a simple graph, and let $\Delta(G)$ and $\chi'(G)$ denote the maximum degree and chromatic index of $G$, respectively. Vizing proved that $\chi'(G)=\Delta(G)$ or $\chi'(G)=\Delta(G)+1$. We say $G$ is $\Delta$-critical if $\chi'(G)=\Delta(G)+1$ and $\chi'(H)<\chi'(G)$ for every proper subgraph $H$ of $G$.
Jinko Kanno, Songling Shan
openaire   +5 more sources

Geometric structure in smooth dual and local Langlands conjecture

This expository paper first reviews some basic facts about p-adic fields, reductive p-adic groups, and the local Langlands conjecture. If G is a reductive p-adic group, then the smooth dual of G is the set of equivalence classes of smooth irreducible ...
Aubert, Anne-Marie, Solleveld, Maarten, Baum, Paul, Plymen, Roger   +3 more
core   +1 more source

On the Hodge conjecture for products of certain surfaces [PDF]

, 2003
In this thesis we prove the Hodge conjecture for products of smooth projective surfaces S(_1) x S(_2), where S(_2) = A is an Abelian surface and S (_1) is such that P(_g)(S(_1)) = 1, q = 2.
J. Ramón Marí, José, J Ramón Marí, José   +1 more
core  

Approximating Vizing's independence number conjecture [PDF]

, 2019
In 1965, Vizing conjectured that the independence ratio of edge-chromatic critical graphs is at most $\frac{1}{2}$. We prove that for every $\epsilon > 0$ this conjecture is equivalent to its restriction on a specific set of edge-chromatic critical ...
Steffen, Eckhard
core   +1 more source

Vizing's Theorem in Rocq

This thesis explores Vizing's theorem in the proof assistant Rocq. We employ the SSReflect language and the open-source Mathematical Components library to extend the graph theory library developed by Christian Doczkal, Damien Pous, and Daniel Severín ...
Grinstead, Kathleen Milligan
core   +3 more sources

Vizing's Conjecture for Almost All Pairs of Graphs

, 2015
For any graph $G=(V,E)$, a subset $S\subseteq V$ $dominates$ $G$ 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 $γ(G)$. In 1963, V.G.
Contractor, Aziz, Krop, Elliot
openaire   +2 more sources

An improved constant for Vizing's conjecture

Algebraic ...
Aliabadi, Mohsen, Krop, Elliot
openaire   +2 more sources