A WZ proof of a “curious” identity.
A invariant for greedoids and antimatroids.
A -ring Frobenius characteristic for .
A σ₃ type condition for heavy cycles in weighted graphs
A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. The weighted degree sum of any three independent vertices is at least m; 2. w(xz) = w(yz) for every...
AB percolation: a brief survey
Abel's method on Summation by Parets and Nonterminating q-Series Identities.
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