Related papers: Homomorphism-homogeneous L-colored graphs

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…

Tension-continuous (shortly TT) mappings are mappings between the edge sets of graphs. They generalize graph homomorphisms. From another perspective, tension-continuous mappings are dual to the notion of flow-continuous mappings and the…

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from edge-coloured graph $G$ to edge-coloured graph $H$ is a vertex-mapping from $G$ to…

In this paper, we state and prove two Fra\"{i}ss\'{e}-style results that cover existence and uniqueness properties for twelve of the eighteen different notions of homomorphism-homogeneity as introduced by Lockett and Truss, and provide…

A graph $G$ is $H$-free if it does not contain an induced subgraph isomorphic to $H$. The study of the typical structure of $H$-free graphs was initiated by Erd\H{o}s, Kleitman and Rothschild, who have shown that almost all $C_3$-free…

For every fixed graph $H$, it is known that homomorphism counts from $H$ and colorful $H$-subgraph counts can be determined in $O(n^{t+1})$ time on $n$-vertex input graphs $G$, where $t$ is the treewidth of $H$. On the other hand, a running…

J. Przytycki has established a connection between the Hochschild homology of an algebra $A$ and the chromatic graph homology of a polygon graph with coefficients in $A$. In general the chromatic graph homology is not defined in the case…

Given graphs $H$ and $G$, possibly with vertex-colors, a homomorphism is a function $f:V(H)\to V(G)$ that preserves colors and edges. Many interesting counting problems (e.g., subgraph and induced subgraph counts) are finite linear…

Let $H$ and $G$ be graphs such that $H$ has at least 3 vertices and is connected. The $H$-line graph of $G$, denoted by $HL(G)$, is that graph whose vertices are the edges of $G$ and where two vertices of $HL(G)$ are adjacent if they are…

We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph $(G,\sigma)$, equipped with lists $L(v) \subseteq V(H), v \in…

We show that feasibility of the $t^\text{th}$ level of the Lasserre semidefinite programming hierarchy for graph isomorphism can be expressed as a homomorphism indistinguishability relation. In other words, we define a class $\mathcal{L}_t$…

Two graphs $G$ and $H$ are homomorphism indistinguishable over a family of graphs $\mathcal{F}$ if for all graphs $F \in \mathcal{F}$ the number of homomorphisms from $F$ to $G$ is equal to the number of homomorphism from $F$ to $H$. Many…

Counting homomorphisms from a graph $H$ into another graph $G$ is a fundamental problem of (parameterized) counting complexity theory. In this work, we study the case where \emph{both} graphs $H$ and $G$ stem from given classes of graphs:…

A graph is said to be {\it total-colored} if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a {\it total monochromatically-connecting coloring} ({\it TMC-coloring}, for short) if any two vertices of…

Given a graph $G$ and a target graph $H$, an $H$-coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$. By appropriate choice of $H$, these colorings can express, for instance, the independent sets or proper vertex colorings…

For graphs $G$ and $H$, a {\em homomorphism} from $G$ to $H$, or {\em $H$-coloring} of $G$, is an adjacency preserving map from the vertex set of $G$ to the vertex set of $H$. Writing ${\rm hom}(G,H)$ for the number of $H$-colorings…

In this paper we describe all edge-colored graphs that are fully symmetric with respect to colors and transitive on every set of edges of the same color. They correspond to fully symmetric homogeneous factorizations of complete graphs. Our…

For graphs $G$ and $H$, an $H$-coloring of $G$ is a function from the vertices of $G$ to the vertices of $H$ that preserves adjacency. $H$-colorings encode graph theory notions such as independent sets and proper colorings, and are a…

Let $\partial_H(u)$ be the set of edges incident with a vertex $u$ in the graph $H$. We say that a graph $G$ is $H$-colorable if there exist total functions $f : E(G) \rightarrow E(H)$ and $g : V(G) \rightarrow V(H)$ such that $f$ is a…

Two plane drawings of graphs on the same set of points are called disjoint compatible if their union is plane and they do not have an edge in common. Let $S$ be a convex point set of $2n \geq 10$ points and let $\mathcal{H}$ be a family of…