Universality of directed graphs of a given height
Universality of separoids
A separoid is a symmetric relation defined on disjoint pairs of subsets of a given set such that it is closed as a filter in the canonical partial order induced by the inclusion (i.e., and ). We introduce the notion of homomorphism as a map which preserve the so-called “minimal Radon partitions” and show that separoids, endowed with these maps, admits an embedding from the category of all finite graphs. This proves that separoids constitute a countable universal partial order. Furthermore,...
Universally image partition regularity.
Universally optimal matrices and field independence of the minimum rank of a graph.
Unmixed bipartite graphs.
Unordered love in infinite directed graphs.
Unpath number of a complete multipartite graph
Untersuchungen zur Minimalbasis nichtprojektiver Graphen.
Updown numbers and the initial monomials of the slope variety.
Up-down permutations of higher order.
Upper and lower bounds for a function related to Brown's Lemma.
Upper and lower bounds for .
Upper bound for the energy of graphs with fixed second and fourth spectral moments
Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices
We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
Upper Bounds for Configurations and Polytopes in Rd
Upper bounds for the domination numbers of toroidal queens graphs
We determine upper bounds for and , the domination and independent domination numbers, respectively, of the graph obtained from the moves of queens on the n×n chessboard drawn on the torus.
Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces
For a graph property and a graph , we define the domination subdivision number with respect to the property to be the minimum number of edges that must be subdivided (where each edge in can be subdivided at most once) in order to change the domination number with respect to the property . In this paper we obtain upper bounds in terms of maximum degree and orientable/non-orientable genus for the domination subdivision number with respect to an induced-hereditary property, total domination...
Upper bounds on the b-chromatic number and results for restricted graph classes
A b-coloring of a graph G by k colors is a proper vertex coloring such that every color class contains a color-dominating vertex, that is, a vertex having neighbors in all other k-1 color classes. The b-chromatic number is the maximum integer k for which G has a b-coloring by k colors. Moreover, the graph G is called b-continuous if G admits a b-coloring by k colors for all k satisfying . In this paper, we establish four general upper bounds on . We present results on the b-chromatic number...
Upper bounds on the non-3-colourability threshold of random graphs.
Upper Bounds on the Signed Total (K, K)-Domatic Number of Graphs
Let G be a graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and Σx∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of distinct signed total k-dominating functions on G with the property that Σdi=1 fi(x) ≤ k for each x ∈ V (G), is called a signed total (k, k)-dominating family (of functions) on G. The maximum number of functions in a signed...