A note on neighbour-distinguishing regular graphs total-weighting.
A note on nested sums.
A Note on Non-Dominating Set Partitions in Graphs
A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S. The cardinality of a minimum dominating (total dominating) set of G is called the domination (total domination) number. A set that does not dominate (totally dominate) G is called a non-dominating (non-total dominating) set of G. A partition of the vertices of G into non-dominating (non-total dominating) sets is...
A note on nonisomorphic Steiner quadruple systems
A note on odd cycle-complete graph Ramsey numbers.
A note on on-line ranking number of graphs
A -ranking of a graph is a mapping such that each path with endvertices of the same colour contains an internal vertex with colour greater than . The ranking number of a graph is the smallest positive integer admitting a -ranking of . In the on-line version of the problem, the vertices of arrive one by one in an arbitrary order, and only the edges of the induced graph are known when the colour for the vertex has to be chosen. The on-line ranking number of a graph is the smallest...
A note on optimality conditions for dual problems to the traveling salesman problem
A note on outerplanarity of product graphs
A note on packing chromatic number of the square lattice.
A note on packing graphs without cycles of length up to five.
A note on packing of two copies of a hypergraph
A 2-packing of a hypergraph 𝓗 is a permutation σ on V(𝓗) such that if an edge e belongs to 𝓔(𝓗), then σ (e) does not belong to 𝓔(𝓗). We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V(𝓗) and has at most 1/2n edges is 2-packable. A 1-uniform hypergraph of order n with more than 1/2n edges shows that this result cannot be improved by increasing the size of 𝓗.
A note on palindromic delta-vectors for certain rational polytopes.
A Note on Path Domination
We study domination between different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in characterizing those graphs in which every uv-walk of one particular kind dominates every uv-walk of other specific kind. We thereby obtained new characterizations of standard graph classes like chordal, interval and superfragile graphs.
A note on perfect matchings in uniform hypergraphs with large minimum collective degree
For an integer and a -uniform hypergraph , let be the largest integer such that every -element set of vertices of belongs to at least edges of . Further, let be the smallest integer such that every -uniform hypergraph on vertices and with contains a perfect matching. The parameter has been completely determined for all and large divisible by by Rödl, Ruci’nski, and Szemerédi in [Perfect matchings in large uniform hypergraphs with large minimum collective degree, submitted]....
A note on periodicity of the 2-distance operator
The paper solves one problem by E. Prisner concerning the 2-distance operator T₂. This is an operator on the class of all finite undirected graphs. If G is a graph from , then T₂(G) is the graph with the same vertex set as G in which two vertices are adjacent if and only if their distance in G is 2. E. Prisner asks whether the periodicity ≥ 3 is possible for T₂. In this paper an affirmative answer is given. A result concerning the periodicity 2 is added.
A note on permutations without runs of given length.
A note on pm-compact bipartite graphs
A graph is called perfect matching compact (briefly, PM-compact), if its perfect matching graph is complete. Matching-covered PM-compact bipartite graphs have been characterized. In this paper, we show that any PM-compact bipartite graph G with δ (G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM-compact, which implies that G is matching-covered
A note on polynomials and -factors of graphs.
A note on -partial difference equations and some applications to generating functions and -integrals
We study the condition on expanding an analytic several variables function in terms of products of the homogeneous generalized Al-Salam-Carlitz polynomials. As applications, we deduce bilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. We also gain multilinear generating functions for the homogeneous generalized Al-Salam-Carlitz polynomials. Moreover, we obtain generalizations of Andrews-Askey integrals and Ramanujan -beta integrals. At last, we derive ...
A note on -colorings of graphs.