Families of triples with high minimum degree are hamiltonian
In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least [...] contains a tight Hamiltonian cycle
Few colored cuts or cycles in edge colored graphs
Finding a minimum dominating set by transforming domination of vertices.
Finding Tricyclic Graphs with a Maximal Number of Matchings - Another Example of Computer Aided Research in Graph Theory
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced...
Forbidden triples implying Hamiltonicity: for all graphs
In [2], Brousek characterizes all triples of graphs, G₁, G₂, G₃, with for some i = 1, 2, or 3, such that all G₁G₂G₃-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁, G₂, G₃, none of which is a , s ≥ 3 such that G₁, G₂, G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In this paper, a characterization will be given of all triples G₁, G₂, G₃ with none being , such that all G₁G₂G₃-free...
Functions on adjacent vertex degrees of trees with given degree sequence
In this note we consider a discrete symmetric function f(x, y) where associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randic index follow as corollaries. The extremal structures...
Functorial concepts of complexity for finite automata.
Further results on the achromatic number
Further results on vertex covering of powers of complete graphs.
General bounds for identifying codes in some infinite regular graphs.
Generalised irredundance in graphs: Nordhaus-Gaddum bounds
For each vertex s of the vertex subset S of a simple graph G, we define Boolean variables p = p(s,S), q = q(s,S) and r = r(s,S) which measure existence of three kinds of S-private neighbours (S-pns) of s. A 3-variable Boolean function f = f(p,q,r) may be considered as a compound existence property of S-pns. The subset S is called an f-set of G if f = 1 for all s ∈ S and the class of f-sets of G is denoted by . Only 64 Boolean functions f can produce different classes , special cases of which include...
Generalized domination, independence and irredudance in graphs
The purpose of this paper is to present some basic properties of 𝓟-dominating, 𝓟-independent, and 𝓟-irredundant sets in graphs which generalize well-known properties of dominating, independent and irredundant sets, respectively.
Generalizing the Ramsey problem through diameter.
Geodetic graphs of diameter two
Geodetic graphs which are homeomorphic to complete graphs
Geometric thickness of complete graphs.
Grad und lokaler Zusammenhang in endlichen Graphen.
Graph connectivity and Wiener index
Graphes de Ramanujan et applications