About a generalization of transversals
The aim of this paper is to generalize several basic results from transversal theory, primarily the theorem of Edmonds and Fulkerson.
About adjoint and -adjoint digraphs of -regular multigraphs. (Sobre digrafos adjuntos y adjuntos de multidigrafos -regulares.)
About division by 1.
About noncommuting graphs.
About the domino problem in the hyperbolic plane from an algorithmic point of view
This paper is a contribution to the general tiling problem for the hyperbolic plane. It is an intermediary result between the result obtained by R. Robinson [Invent. Math.44 (1978) 259–264] and the conjecture that the problem is undecidable.
About uniquely colorable mixed hypertrees
A mixed hypergraph is a triple 𝓗 = (X,𝓒,𝓓) where X is the vertex set and each of 𝓒, 𝓓 is a family of subsets of X, the 𝓒-edges and 𝓓-edges, respectively. A k-coloring of 𝓗 is a mapping c: X → [k] such that each 𝓒-edge has two vertices with the same color and each 𝓓-edge has two vertices with distinct colors. 𝓗 = (X,𝓒,𝓓) is called a mixed hypertree if there exists a tree T = (X,𝓔) such that every 𝓓-edge and every 𝓒-edge induces a subtree of T. A mixed hypergraph 𝓗 is called uniquely...
Abschätzung der Dichte von Summenmengen.
Accelerated series for universal constants, by the WZ method.
Achieving snaky.
Achromatic number of for small
The achromatic number of a graph is the maximum number of colours in a proper vertex colouring of such that for any two distinct colours there is an edge of incident with vertices of those two colours. We determine the achromatic number of the Cartesian product of and for all .
Actions of the symmetric group generated by comparable sets of integers and Smith invariants.
Acyclic 4-choosability of planar graphs without 4-cycles
A proper vertex coloring of a graph is acyclic if there is no bicolored cycle in . In other words, each cycle of must be colored with at least three colors. Given a list assignment , if there exists an acyclic coloring of such that for all , then we say that is acyclically -colorable. If is acyclically -colorable for any list assignment with for all , then is acyclically -choosable. In 2006, Montassier, Raspaud and Wang conjectured that every planar graph without 4-cycles...
Acyclic 6-Colouring of Graphs with Maximum Degree 5 and Small Maximum Average Degree
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
Acyclic chromatic index of a graph with maximum valency three
Acyclic chromatic index of a subdivided graph
Acyclic digraphs and eigenvalues of -matrices.
Acyclic numbers of graphs.
Acyclic reducible bounds for outerplanar graphs
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. 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 and 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 -majority tournaments.