A survey of minimum saturated graphs.
A theorem on -connected graphs
A theorem on Hamiltonian line graphs
A Turán type problem concerning the powers of the degrees of a graph.
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...
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 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,...
Algebraic connectivity of graphs
Algèbre linéaire et cheminement dans un graphe
Algorithm 45. A heuristic algorithm for the traveling-salesman problem
Algorithmes de plus courts chemins pour traiter des données floues
Almost every bipartite graph has not two vertices of minimum degree
An almost naive algorithm for finding relative neighbourhood graphs in metrics
An application of set-pair systems for multitransversals
An entropy proof of the Kahn-Lovász theorem.
An exact performance bound for an time greedy matching procedure.
An extremal characterization of projective planes.
An extremal problem for some classes of oriented graphs
An extremal problem on potentially -graphic sequences.
An extremal property of Turán graphs.