In this paper we survey results and open problems on the structure of additive and
hereditary properties of graphs. The important role of vertex partition problems, in particular …

Let τ (G) denote the number of vertices in a longest path of the graph G and let k₁ and k₂
be positive integers such that τ (G)= k₁+ k₂. The question at hand is whether the vertex set …

For a simple graph H,→ H denotes the class of all graphs that admit homomorphisms to H
(such classes of graphs are called hom-properties). We investigate hom-properties from the …

The study and recognition of graph families (or graph properties) is an essential part of
combinatorics. Graph colouring is another fundamental concept of graph theory that can be …

GRAPHS MAXIMAL WITH RESPECT TO ABSENCE OF HAMILTONIAN PATHS Page 1
Discussiones Mathematicae Graph Theory 18 (1998) 205–208 GRAPHS MAXIMAL WITH …

The Path Partition Conjecture (PPC) states that if G is any graph and (λ 1, λ 2) any pair of
positive integers such that G has no path with more than λ 1+ λ 2 vertices, then there exists a …

An additive hereditary graph property is a set of graphs, closed under isomorphism and
under taking subgraphs and disjoint unions. Let ${\cal P} _1,>...,{\cal P} _n $ be additive …

Let ₁,..., ₙ be properties of graphs. A (₁,..., ₙ)-partition of a graph G is a partition V₁,..., Vₙ
of V (G) such that, for each i= 1,..., n, the subgraph of G induced by V_i has property _i. If a …

Let L^a denote a set of additive hereditary graph properties. It is a known fact that a partially
ordered set (L^a,⊆) is a complete distributive lattice. We present results when a join of two …

Пусть G=(V, E)—конечный неориентированный граф. Число вершин в наиболее
длинном пути графа G будем обозначать через τ (G). Через g (G) и c (G) будем …