Related papers: Connected forcing density and related problems
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
For a graph $G = (V, E)$, the $\gamma$-graph of $G$, denoted $G(\gamma) = (V(\gamma), E(\gamma))$, is the graph whose vertex set is the collection of minimum dominating sets, or $\gamma$-sets of $G$, and two $\gamma$-sets are adjacent in…
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed that the maximum anti-forcing number of $G$ is no more than the cyclomatic number. In this paper, we get a novel upper bound on the maximum anti-forcing number of $G$…
Many concrete problems are formulated in terms of a finite set of points in $R^n$ which, via the ambient Euclidean metric, becomes a finite metric space. To obtain information from such a space, it is often useful to associate a graph to…
An edge-colored graph $G$ is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph $G$, denoted by…
In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph…
We investigate when limits of graphs (graphons) and permutations (permutons) are uniquely determined by finitely many densities of their substructures, i.e., when they are finitely forcible. Every permuton can be associated with a graphon…
Given a set $\mathcal{F}$ of graphs, a graph $G$ is $\mathcal{F}$-free if $G$ does not contain any member of $\mathcal{F}$ as an induced subgraph. Barrus, Kumbhat, and Hartke [M. D. Barrus, M. Kumbhat, and S. G. Hartke, Graph classes…
Let $ G=(V,E) $ be a simple graph of order $ n $ and size $ m $. A connected edge cover set of a graph is a subset $S$ of edges such that every vertex of the graph is incident to at least one edge of $S$ and the subgraph induced by $S$ is…
Zero forcing is a one-player game played on a graph. The player chooses some set of vertices to color, then iteratively applies a color change rule: If all but one of a colored vertex's neighbors are colored, color (i.e. "force") the…
Let $G$ be a graph and let $f$ be a positive integer-valued function on $V(G)$. Assume that for all $S\subseteq V(G)$, $$\sum_{v\in I(G\setminus S)}f(v)(f(v)+1)\le |S|,$$ where $I(G\setminus S)$ denotes the set of isolated vertices of…
Recently, there have been found new relations between the zero forcing number and the minimum rank of a graph with the algebraic co-rank. We continue on this direction by giving a characterization of the graphs with real algebraic co-rank…
An independent set in a graph G is a set of vertices no two of which are joined by an edge. A vertex-weighted graph associates a weight with every vertex in the graph. A vertex-weighted graph G is called a unique independence…
A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough. A graph is minimally $t$-tough if…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
Edge connectivity and vertex connectivity are two fundamental concepts in graph theory. Although by now there is a good understanding of the structure of graphs based on their edge connectivity, our knowledge in the case of vertex…
Monotone trees - trees with a function defined on their vertices that decreases the further away from a root node one travels, are a natural model for a process that weakens the further one gets from its source. Given an aggregation of…
In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…