Rigid undirected graphs with given number of vertices
Universality of directed graphs of a given height
Some Results on the Oberwolfach Problem. (Decomposition of Completet Graphs into Isomorphic Quadratic Factors).
Some Results on the Oberwolfach Problem. (Decomposition of Complete Graphs into Isomorphic Quadratic Factors). (Short Communication).
On the Complexity of the 3-Kernel Problem in Some Classes of Digraphs
Let D be a digraph with the vertex set V (D) and the arc set A(D). A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V (D) − N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and (k − 1)-absorbent subset of V (D). A 2-kernel is called a kernel. It is known that the problem of determining whether a digraph has a kernel (“the kernel problem”) is NP-complete, even in quite restricted...
Three-and-more set theorems
In this paper we generalize classical 3-set theorem related to stable partitions of arbitrary mappings due to Erdős-de Bruijn, Katětov and Kasteleyn. We consider a structural generalization of this result to partitions preserving sets of inequalities and characterize all finite sets of such inequalities which can be preserved by a “small” coloring. These results are also related to graph homomorphisms and (oriented) colorings.
Matrix partitions with finitely many obstructions.
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