On a novel critically-sampled discrete-time real Gabor transform
9
Citation
12
Reference
10
Related Paper
Citation Trend
Keywords:
Sequence (biology)
The Steiner n -antipodal graph of a graph G on p vertices, denoted by S A n ( G ), has the same vertex set as G and any n (2 ≤ n ≤ p ) vertices are mutually adjacent in S A n ( G ) if and only if they are n -antipodal in G . When G is disconnected, any n vertices are mutually adjacent in S A n ( G ) if not all of them are in the same component. S A n ( G ) coincides with the antipodal graph A ( G ) when n = 2 . The least positive integer n such that S A n ( G ) ≅ H , for a pair of graphs G and H on p vertices, is called the Steiner A -completion number of G over H . When H = K p , the Steiner A -completion number of G over H is called the Steiner antipodal number of G . In this article, we obtain the Steiner antipodal number of some families of graphs and for any tree. For every positive integer k , there exists a tree having Steiner antipodal number k and there exists a unicyclic graph having Steiner antipodal number k . Also we show that the notion of the Steiner antipodal number of graphs is independent of the Steiner radial number, the domination number and the chromatic number of graphs.
Antipodal point
Steiner tree problem
Cite
Citations (3)
A bipartite graph G = (U; V;E) is doubly convex if all its vertices from the U can be numbered 1, 2,..., |U| and all vertices from V can be numbered 1, 2,…, |V| in such a way that for any vertex of G the set of numbers assigned to neighbors is an interval of integers. An interval total t-coloring of a graph G is a total coloring of G with colors 1, 2,…,t such that at least one vertex or edge of G is colored by i; i = 1, 2,…,t, and the edges incident to each vertex v together with v are colored by dG(v)+1 consecutive colors, where dG(v) is the degree of a vertex v in G. In this paper we prove that all doubly convex bipartite graphs have an interval total coloring. Furthermore, we give some bounds for the minimum and the maximum span in interval total colorings of these graphs.
Total coloring
Complete coloring
Edge Coloring
Fractional coloring
Cite
Citations (2)
In this paper,two operators are defined,and their underlying properties are found,then the R-dual relationship is classified from the aspect of the operators defined.Furthermore,the commutability of the bases of constructing R-dual sequence is discussed.In particular,SR-dual sequence is defined and is clarified.At last an example is given.
Sequence (biology)
Cite
Citations (0)
Dual purpose
Cite
Citations (8)
Consider a graph $G$ with chromatic number $k$ and a collection of complete bipartite graphs, or bicliques, that cover the edges of $G$. We prove the following two results: $\bullet$ If the bipartite graphs form a partition of the edges of $G$, then their number is at least $2^{\sqrt{\log_2 k}}$. This is the first improvement of the easy lower bound of $\log_2 k$, while the Alon-Saks-Seymour conjecture states that this can be improved to $k-1$. $\bullet$ The sum of the orders of the bipartite graphs in the cover is at least $(1-o(1))k\log_2 k$. This generalizes, in asymptotic form, a result of Katona and Szemerédi who proved that the minimum is $k\log_2 k$ when $G$ is a clique.
Complete bipartite graph
Clique
Cite
Citations (6)
If $G$ is a graph and $\mathcal{H}$ is a set of subgraphs of $G$, we say that an edge-coloring of $G$ is $\mathcal{H}$-polychromatic if every graph from $\mathcal{H}$ gets all colors present in $G$ on its edges. The $\mathcal{H}$-polychromatic number of $G$, denoted $\operatorname{poly}_\mathcal{H} (G)$, is the largest number of colors in an $\mathcal{H}$-polychromatic coloring. In this paper we determine $\operatorname{poly}_\mathcal{H} (G)$ exactly when $G$ is a complete graph on $n$ vertices, $q$ is a fixed nonnegative integer, and $\mathcal{H}$ is one of three families: the family of all matchings spanning $n-q$ vertices, the family of all $2$-regular graphs spanning at least $n-q$ vertices, and the family of all cycles of length precisely $n-q$. There are connections with an extension of results on Ramsey numbers for cycles in a graph.
Ramsey's theorem
Cite
Citations (0)
A set of vertices C in a graph is convex if it contains all vertices which lie on shortest paths between vertices in C. The convex hull of a set of vertices S is the smallest convex set containing S. The hull number $h(G)$ of a graph G is the smallest cardinality of a set of vertices whose convex hull is the vertex set of G. For a connected triangle-free graph G of order n and diameter d at least 4, we prove that $h(G)\leq(n-d+3)/3$ if G has minimum degree at least 3 and that $h(G)\leq2(n-d+5)/7$, if G is cubic. Furthermore for a connected graph G of order n, girth g at least 5, minimum degree at least 2, and diameter d, we prove $h(G)\leq2+(n-d-1)/\left\lceil\frac{g-1}{2}\right\rceil$. All bounds are best possible.
Bound graph
Cite
Citations (44)
Rainbow
Disjoint sets
Complete bipartite graph
Edge Coloring
Cite
Citations (7)
Complete bipartite graph
Cite
Citations (15)