Related papers: Complements of graphs of meromorphic functions and…

We say that a graph $H$ dominates another graph $H'$ if the number of homomorphisms from $H'$ to any graph $G$ is dominated, in an appropriate sense, by the number of homomorphisms from $H$ to $G$. We study the family of dominating graphs,…

Let $G$ be a graph. A set $S$ of vertices in $G$ dominates the graph if every vertex of $G$ is either in $S$ or a neighbor of a vertex in $S$. Finding a minimal cardinality set which dominates the graph is an NP-complete problem. The graph…

Let D_1 be a subdomain of D_2 in the complex plane CC. Under very mild conditions on D_2 we show that there exist holomorphic functions f, defined on D_1 with the property that $f$ is nowhere extendible across the boundary of D_1, while the…

Let $\gamma(G)$ and $\gamma_t(G)$ denote the domination number and the total domination number, respectively, of a graph $G$ with no isolated vertices. It is well-known that $\gamma_t(G) \leq 2\gamma(G)$. We provide a characterization of a…

Ho proved in [A note on the total domination number, Util.Math. 77 (2008) 97--100] that the total domination number of the Cartesian product of any two graphs with no isolated vertices is at least one half of the product of their total…

Understanding graph density profiles is notoriously challenging. Even for pairs of graphs, complete characterizations are known only in very limited cases, such as edges versus cliques. This paper explores a relaxation of the graph density…

Structural stability of holomorphic functions has been the subject of much research in the last fifty years. Due to various technicalities, however, most of that work has focused on so-called finite-type functions (functions whose set of…

A graph is said to be well-dominated if all its minimal dominating sets are of the same size. The class of well-dominated graphs forms a subclass of the well studied class of well-covered graphs. While the recognition problem for the class…

We study stable finiteness of extensions of 2-graph C*-algebras determined by saturated hereditary sets of vertices. We use two iterations of the Pimsner-Voiculescu sequence to calculate the map in K-theory induced by the inclusion of a…

The dominating graph of a graph G is a graph whose vertices correspond to the dominating sets of G and two vertices are adjacent whenever their corresponding dominating sets differ in exactly one vertex. Studying properties of dominating…

We develop a space-level refinement of the $2$-factor homology by constructing a stable homotopy type associated to a certain family $\mathscr{G}$ of planar trivalent graphs equipped with perfect matchings. Specifically, we define a cover…

A graph is \emph{well-dominated} if all of its minimal dominating sets have the same cardinality. We prove that at least one of the factors is well-dominated if the Cartesian product of two graphs is well-dominated. In addition, we show…

Counting dominating sets in a graph $G$ is closely related to the neighborhood complex of $G$. We exploit this relation to prove that the number of dominating sets $d(G)$ of a graph is determined by the number of complete bipartite…

Many questions at the core of graph theory can be formulated as questions about certain group-valued flows: examples are the cycle double cover conjecture, Berge-Fulkerson conjecture, and Tutte's 3-flow, 4-flow, and 5-flow conjectures. As…

Given a simple graph $G$ on $n$ vertices, a subset of vertices $U \subseteq V(G)$ is dominating if every vertex of $V(G)$ is either in $U$ or adjacent to a vertex of $U$. The domination polynomial of $G$ is the generating function whose…

A family T of digraphs is a complete set of obstructions for a digraph H if for an arbitrary digraph G the existence of a homomorphism from G to H is equivalent to the non-existence of a homomorphism from any member of T to G. A digraph H…

Let $G_1$ and $G_2$ be disjoint copies of a graph $G$, and let $f: V(G_1) \rightarrow V(G_2)$ be a function. Then a \emph{functigraph} $C(G, f)=(V, E)$ has the vertex set $V=V(G_1) \cup V(G_2)$ and the edge set $E=E(G_1) \cup E(G_2) \cup…

In this paper, we establish a general second main theorem for meromorphic mappings from $\mathbb C^m$ into a subvariety $V$ of $\mathbb P^n(\mathbb C)$ with respect to an arbitrary family of slowly moving hypersurfaces $\mathcal…

We complete and precise the results of [B.13] and we prove a strong version of the semi-proper direct image theorem with values in the space C f n (M) of finite type closed n--cycles in a complex space M. We describe the strongly…

We prove that if a polynomial vector field on C2 has a proper and non-algebraic trajectory analytically isomorphic to C* all its trajectories are proper, and except at most one which is contained in an algebraic curve of type C all of them…