A note on symmetric powers of the standard representation of .
A note on -designs with intersection numbers.
A note on the asymptotic and computational complexity of graph distinguishability.
A note on the chromatic number of the alternative negation of two graphs
A note on the Chvátal-rank of clique family inequalities
Clique family inequalities a∑v∈W xv + (a - 1)∈v∈W, xv ≤ aδ form an intriguing class of valid inequalities for the stable set polytopes of all graphs. We prove firstly that their Chvátal-rank is at most a, which provides an alternative proof for the validity of clique family inequalities, involving only standard rounding arguments. Secondly, we strengthen the upper bound further and discuss consequences regarding the Chvátal-rank of subclasses of claw-free graphs.
A note on the circumference of graphs.
A note on the component structure in random intersection graphs with tunable clustering.
A note on the computational complexity of computing the edge rotation distance between graphs
A note on the critical group of a line graph.
A note on the cubical dimension of new classes of binary trees
The cubical dimension of a graph is the smallest dimension of a hypercube into which is embeddable as a subgraph. The conjecture of Havel (1984) claims that the cubical dimension of every balanced binary tree with vertices, , is . The 2-rooted complete binary tree of depth is obtained from two copies of the complete binary tree of depth by adding an edge linking their respective roots. In this paper, we determine the cubical dimension of trees obtained by subdividing twice a 2-rooted...
A note on the derived semifield planes of order 16.
A note on the determinant of a Toeplitz-Hessenberg matrix
The nth-order determinant of a Toeplitz-Hessenberg matrix is expressed as a sum over the integer partitions of n. Many combinatorial identities involving integer partitions and multinomial coefficients can be generated using this formula.
A note on the distance-balanced property of generalized Petersen graphs.
A note on the distribution of the three types of nodes in uniform binary trees.
A note on the domination number of a graph and its complement
If is a simple graph of size without isolated vertices and is its complement, we show that the domination numbers of and satisfy where is the minimum degree of vertices in .
A note on the double Roman domination number of graphs
For a graph , a double Roman dominating function is a function having the property that if , then the vertex must have at least two neighbors assigned under or one neighbor with , and if , then the vertex must have at least one neighbor with . The weight of a double Roman dominating function is the sum . The minimum weight of a double Roman dominating function on is called the double Roman domination number of and is denoted by . In this paper, we establish a new upper bound...
A note on the edge-connectivity of cages.
A note on the exact expected length of the th part of a random partition.
A note on the Folkman number
A note on the graph equation .