A note on domatically critical and cocritical graphs
A note on domination in bipartite graphs
DOMINATING SET remains NP-complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed.
A note on domination parameters in random graphs
Domination parameters in random graphs G(n,p), where p is a fixed real number in (0,1), are investigated. We show that with probability tending to 1 as n → ∞, the total and independent domination numbers concentrate on the domination number of G(n,p).
A note on domination parameters of the conjunction of two special graphs
A dominating set D of G is called a split dominating set of G if the subgraph induced by the subset V(G)-D is disconnected. The cardinality of a minimum split dominating set is called the minimum split domination number of G. Such subset and such number was introduced in [4]. In [2], [3] the authors estimated the domination number of products of graphs. More precisely, they were study products of paths. Inspired by those results we give another estimation of the domination number of the conjunction...
A note on domino shuffling.
A note on domino treewidth.
A note on edge-colourings avoiding rainbow and monochromatic .
A note on embedding hypertrees.
A note on face coloring entire weightings of plane graphs
Given a weighting of all elements of a 2-connected plane graph G = (V,E, F), let f(α) denote the sum of the weights of the edges and vertices incident with the face _ and also the weight of _. Such an entire weighting is a proper face colouring provided that f(α) ≠ f(β) for every two faces α and _ sharing an edge. We show that for every 2-connected plane graph there is a proper face-colouring entire weighting with weights 1 through 4. For some families we improved 4 to 3
A Note on Generalized Line Graphs
A note on graph coloring
A note on graph coloring extensions and list-colorings.
A note on graph colouring
A Note On Graphs Representable As Product Graphs
A note on graphs with two main eigenvalues
A note on graphs without short even cycles.
A note on Hamiltonian cycles in generalized Halin graphs
We show that every 2-connected (2)-Halin graph is Hamiltonian.
A note on intersecting graphs.
A note on intersection dimensions of graph classes
The intersection dimension of a graph with respect to a class of graphs is the minimum such that is the intersection of some graphs on the vertex set belonging to . In this paper we follow [ Kratochv’ıl J., Tuza Z.: Intersection dimensions of graph classes, Graphs and Combinatorics 10 (1994), 159–168 ] and show that for some pairs of graph classes , the intersection dimension of graphs from with respect to is unbounded.
A note on joins of additive hereditary graph properties
Let denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in has a finite or infinite family of minimal forbidden subgraphs.