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.
A note on radio antipodal colourings of paths
The radio antipodal number of a graph is the smallest integer such that there exists an assignment satisfying for every two distinct vertices and of , where is the diameter of . In this note we determine the exact value of the antipodal number of the path, thus answering the conjecture given in [G. Chartrand, D. Erwin and P. Zhang, Math. Bohem. 127 (2002), 57–69]. We also show the connections between this colouring and radio labelings.
A note on random minimum length spanning trees.
A note on randomly complete -partite graphs
A note on rational succession rules.
A note on reconstructing of finite trees from small subtrees
A note on rectilinearity and angular resolution.
A note on removing a point of a strong digraph