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.
A note on -free precolouring with colours.
A note on kernels and solutions in digraphs
For given nonnegative integers k,s an upper bound on the minimum number of vertices of a strongly connected digraph with exactly k kernels and s solutions is presented.
A note on (k,l)-kernels in B-products of graphs
B-products of graphs and their generalizations were introduced in [4]. We determined the parameters k, l of (k,l)-kernels in generalized B-products of graphs. These results are generalizations of theorems from [2].
A note on k-uniform self-complementary hypergraphs of given order
We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if is even.
A note on line colorings of cubic graphs
A note on line graphs
A note on linear discrepancy.
A note on link graphs
A Note on Longest Paths in Circular Arc Graphs
As observed by Rautenbach and Sereni [SIAM J. Discrete Math. 28 (2014) 335-341] there is a gap in the proof of the theorem of Balister et al. [Combin. Probab. Comput. 13 (2004) 311-317], which states that the intersection of all longest paths in a connected circular arc graph is nonempty. In this paper we close this gap.
A note on major sequences and external activity in trees.
A note on maximal common subgraphs of the Dirac's family of graphs
Let ⁿ be a given set of unlabeled simple graphs of order n. A maximal common subgraph of the graphs of the set ⁿ is a common subgraph F of order n of each member of ⁿ, that is not properly contained in any larger common subgraph of each member of ⁿ. By well-known Dirac’s Theorem, the Dirac’s family ⁿ of the graphs of order n and minimum degree δ ≥ [n/2] has a maximal common subgraph containing Cₙ. In this note we study the problem of determining all maximal common subgraphs of the Dirac’s family...
A note on maximal -degenerate graphs