Distance minimale entre partitions et préordonnances dans un ensemble fini
Distance of Thorny Graphs
Distance perfectness of graphs
In this paper, we propose a generalization of well known kinds of perfectness of graphs in terms of distances between vertices. We introduce generalizations of α-perfect, χ-perfect, strongly perfect graphs and we establish the relations between them. Moreover, we give sufficient conditions for graphs to be perfect in generalized sense. Other generalizations of perfectness are given in papers [3] and [7].
Distance spectral radius of trees with fixed maximum degree.
Distance-Locally Disconnected Graphs
For an integer k ≥ 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ∈ V (G), the set of vertices at distance at least 1 and at most k from x induces in G a disconnected graph. In this paper we study the asymptotic behavior of the number of edges of a k-locally disconnected graph on n vertices. For general graphs, we show that this number is Θ(n2) for any fixed value of k and, in the special case of regular graphs,...
Distances between directed graphs
Distances between partially ordered sets
A distance between finite partially ordered sets is studied. It is a certain measure of the difference of their structure.
Distances between rooted trees
Two types of a distance between isomorphism classes of graphs are adapted for rooted trees.
Distances in random graphs with finite mean and infinite variance degrees.
Distances invariantes et L-cliques sur certains demi-groupes finis
Distances on the tropical line determined by two points
Let and be points in . Write if is a multiple of . Two different points and in uniquely determine a tropical line passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on leaves. It is also a metric graph. If some representatives and of and are the first and second columns of some real normal idempotent order matrix , we prove that the tree is described by a matrix , easily obtained from . We also prove that...
Distinct distances in graph drawings.
Distinct equilateral triangle dissections of convex regions
We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist. We also provide necessary and sufficient conditions for some convex...
Distinguishability of locally finite trees.
Distinguishing Cartesian powers of graphs.
Distinguishing Cartesian Products of Countable Graphs
The distinguishing number D(G) of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism. In this paper we improve results about the distinguishing number of Cartesian products of finite and infinite graphs by removing restrictions to prime or relatively prime factors.
Distinguishing chromatic numbers of bipartite graphs.
Distinguishing graphs by the number of homomorphisms
A homomorphism from one graph to another is a map that sends vertices to vertices and edges to edges. We denote the number of homomorphisms from G to H by |G → H|. If 𝓕 is a collection of graphs, we say that 𝓕 distinguishes graphs G and H if there is some member X of 𝓕 such that |G → X | ≠ |H → X|. 𝓕 is a distinguishing family if it distinguishes all pairs of graphs. We show that various collections of graphs are a distinguishing family.
Distinguishing infinite graphs.
Distinguishing maps.