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Acyclic 6-Colouring of Graphs with Maximum Degree 5 and Small Maximum Average Degree

Anna Fiedorowicz (2013)

Discussiones Mathematicae Graph Theory

A k-colouring of a graph G is a mapping c from the set of vertices of G to the set {1, . . . , k} of colours such that adjacent vertices receive distinct colours. Such a k-colouring is called acyclic, if for every two distinct colours i and j, the subgraph induced by all the edges linking a vertex coloured with i and a vertex coloured with j is acyclic. In other words, every cycle in G has at least three distinct colours. Acyclic colourings were introduced by Gr¨unbaum in 1973, and since then have...

Acyclic chromatic index and linear arboricity of graphs

Filip Guldan (1991)

Mathematica Slovaca

Acyclic chromatic index of a graph with maximum valency three

Jozef Fiamčík (1980)

Archivum Mathematicum

Acyclic chromatic index of a subdivided graph

Jozef Fiamčík (1984)

Archivum Mathematicum

Acyclic digraphs and eigenvalues of $(0, 1)$ -matrices.

McKay, Brendan D., Oggier, Frédérique E., Royle, Gordon F., Sloane, N.J.A., Wanless, Ian M., Wilf, Herbert S. (2004)

Journal of Integer Sequences [electronic only]

Acyclic numbers of graphs.

Samodivkin, Vladmir (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Acyclic reducible bounds for outerplanar graphs

Mieczysław Borowiecki, Anna Fiedorowicz, Mariusz Hałuszczak (2009)

Discussiones Mathematicae Graph Theory

For a given graph G and a sequence ₁, ₂,..., ₙ of additive hereditary classes of graphs we define an acyclic (₁, ₂,...,Pₙ)-colouring of G as a partition (V₁, V₂,...,Vₙ) of the set V(G) of vertices which satisfies the following two conditions: 1. $G [V_{i}] \in_{i}$ for i = 1,...,n, 2. for every pair i,j of distinct colours the subgraph induced in G by the set of edges uv such that $u \in V_{i}$ and $v \in V_{j}$ is acyclic. A class R = ₁ ⊙ ₂ ⊙ ... ⊙ ₙ is defined as the set of the graphs having an acyclic (₁, ₂,...,Pₙ)-colouring. If ⊆ R,...

Acyclic sets in $k$ -majority tournaments.

Milans, Kevin G., Schreiber, Daniel H., West, Douglas B. (2011)

The Electronic Journal of Combinatorics [electronic only]

Acyclic, star and oriented colourings of graph subdivisions.

Wood, David R. (2005)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Adaptive identification in Torii in the King lattice.

Ben-Haim, Yael, Gravier, Sylvain, Lobstein, Antoine, Moncel, Julien (2011)

The Electronic Journal of Combinatorics [electronic only]

Adaptive tracking via pinning in networks of nonidentical nodes

Juan Gonzalo Barajas-Ramírez (2018)

Kybernetika

We investigate the control of dynamical networks for the case of nodes, that although different, can be make passive by feedback. The so-called V-stability characterization allows for a simple set of stabilization conditions even in the case of nonidentical nodes. This is due to the fact that under V-stability characterization the dynamical difference between node of a network reduces to their different passivity degrees, that is, a measure of the required feedback gain necessary to make the node...

Addendum and erratum to the paper "On the size of a maximal induced tree in a random graph"

Michał Karoński, Zbigniew Palka (1981)

Mathematica Slovaca

Addendum to : “Prime graph components of finite almost simple groups” [Rend. Sem. Mat. Univ. Padova 102 (1999), 1–22]

Maria Silvia Lucido (2002)

Rendiconti del Seminario Matematico della Università di Padova

Addendum to “Ring elements as sums of units”

Charles Lanski, Attila Maróti (2013)

Open Mathematics

We give a comment to Theorem 1.1 published in our paper “Ring elements as sums of units” [Cent. Eur. J. Math., 2009, 7(3), 395–399].

Adding $\pm 1$ to the argument of a Hall-Littlewood polynomial.

Lascoux, Alain (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

Adding layers to bumped-body polyforms with minimum perimeter preserves minimum perimeter.

Yang, Winston C. (2006)

The Electronic Journal of Combinatorics [electronic only]

Additive decomposition of matrices under rank conditions and zero pattern constraints

Harm Bart, Torsten Ehrhardt (2022)

Czechoslovak Mathematical Journal

This paper deals with additive decompositions $A = A_{1} + \dots + A_{p}$ of a given matrix $A$ , where the ranks of the summands $A_{1}, ..., A_{p}$ are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.

Additive functions on trees

Piroska Lakatos (2001)

Colloquium Mathematicae

The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see I. Reiten [R]) and applications of additive functions in representation theory (see H. Lenzing and I. Reiten [LR] and T. Hübner [H]). We consider graphs equipped with integer-valued functions, i.e. valued graphs (see also [DR]). Methods are given for constructing additive functions on valued trees (in particular on Euclidean graphs) and for characterizing...

Additive rank-one nonincreasing maps on Hermitian matrices over the field $G F (2^{2})$ .

Orel, Marko, Kuzma, Bojan (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Adjacency matrix equations and related problems: Research notes

Maciej M. Sysło (1983)

Commentationes Mathematicae Universitatis Carolinae

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