Related papers: Minimum Cost Homomorphisms to Semicomplete Multipa…

Given a graph $H$, we investigate the $d$-regular graphs $G$ with the highest $H$-density. We reframe the problem as a continuous optimization problem on the eigenvalues of $G$ by relating injective homomorphism numbers from $H$ and…

A locally surjective homomorphism from a graph $G$ to a graph $H$ is an edge-preserving mapping from $V(G)$ to $V(H)$ that is surjective in the neighborhood of each vertex in $G$. In the list locally surjective homomorphism problem, denoted…

The diffeomorphic registration framework enables to define an optimal matching function between two probability measures with respect to a data-fidelity loss function. The non convexity of the optimization problem renders the choice of this…

Let $\mu$ be a metric on a set T, and let c be a nonnegative function on the unordered pairs of elements of a superset $V\supseteq T$. We consider the problem of minimizing the inner product $c\cdot m$ over all semimetrics m on V such that…

The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This…

Given an $n$-vertex pseudorandom graph $G$ and an $n$-vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, i.e.\ an embedding $\varphi\colon V(H)\to V(G)$ so that $\varphi(u)\varphi(v)\in E(G)$ for all…

The minimum-cost subset $k$-connected subgraph problem is a cornerstone problem in the area of network design with vertex connectivity requirements. In this problem, we are given a graph $G=(V,E)$ with costs on edges and a set of terminals…

Motivated by multipath routing, we introduce a multi-connected variant of spanners. For that purpose we introduce the $p$-multipath cost between two nodes $u$ and $v$ as the minimum weight of a collection of $p$ internally vertex-disjoint…

A bipartite graph $G=(U,V,E)$ is convex if the vertices in $V$ can be linearly ordered such that for each vertex $u\in U$, the neighbors of $u$ are consecutive in the ordering of $V$. An induced matching $H$ of $G$ is a matching such that…

The $\mathcal{H}$-coloring problem for undirected simple graphs is a computational problem from a huge class of the constraint satisfaction problems (CSP): an $\mathcal{H}$-coloring of a graph $\mathcal{G}$ is just a homomorphism from…

An out-branching $B^+_u$ (in-branching $B^-_u$) in a digraph $D$ is a connected spanning subdigraph of $D$ in which every vertex except the vertex $u$, called the root, has in-degree (out-degree) one. A {\bf good $\mathbf{(u,v)}$-pair} in…

Given a graph $G=(V,E)$ with costs on its edges, the minimum-cost edge cover problem consists of finding a subset of $E$ covering all vertices in $V$ at minimum cost. If $G$ is bipartite, this problem can be solved in time $O(|V|^3)$ via a…

A typical Dirac-type problem in extremal graph theory is to determine the minimum degree threshold for a graph $G$ to have a spanning subgraph $H$, e.g. the Dirac theorem. A natural following up problem would be to seek an $H$-factor, which…

We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time…

The interplay of minimum degree conditions and structural properties of large graphs with forbidden subgraphs is a central topic in extremal graph theory. For a given graph $F$ we define the homomorphism threshold as the infimum over all…

For graphs $G$ and $H$, a homomorphism from $G$ to $H$, or $H$-coloring of $G$, is a map from the vertices of $G$ to the vertices of $H$ that preserves adjacency. When $H$ is composed of an edge with one looped endvertex, an $H$-coloring of…

In the Survivable Network Design Problem (SNDP), the input is an edge-weighted (di)graph $G$ and an integer $r_{uv}$ for every pair of vertices $u,v\in V(G)$. The objective is to construct a subgraph $H$ of minimum weight which contains…

Let $G$ and $H$ be two simple graphs. A bijection $\phi:V(G)\rightarrow V(H)$ is called an isomorphism between $G$ and $H$ if $(\phi v_i)(\phi v_j)\in E(H)$ $\Leftrightarrow$ $v_i v_j\in E(G)$, $\forall v_i,v_j \in V(G)$. In the case that…

The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…

A bipartite graph is chordal bipartite if every cycle of length at least six has a chord in it. M$\ddot{\rm u}$ller \cite {muller1996Hamiltonian} has shown that the Hamiltonian cycle problem is NP-complete on chordal bipartite graphs by…