Related papers: Graphs Identified by Logics with Counting
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
This note presents several results in graph theory inspired by the author's work in the proof theory of linear logic; these results are purely combinatorial and do not involve logic. We show that trails avoiding forbidden transitions,…
The $k$-dominating graph $D_k(G)$ of a graph $G$ is defined on the vertex set consisting of dominating sets of $G$ with cardinality at most $k$, two such sets being adjacent if they differ by either adding or deleting a single vertex. A…
Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit…
K\"onig's edge coloring theorem says that a bipartite graph with maximal degree $n$ has an edge coloring with no more than $n$ colors. We explore the computability theory and Reverse Mathematics aspects of this theorem. Computable bipartite…
A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
Let F be a set of ordered patterns, i.e., graphs whose vertices are linearly ordered. An F-free ordering of the vertices of a graph H is a linear ordering of V(H) such that none of patterns in F occurs as an induced ordered subgraph. We…
Following a general program of studying limits of discrete structures, and motivated by the theory of limit objects of converge sequences of dense simple graphs, we study the limit of graph sequences such that every edge is labeled by an…
We study the properties of finite graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to some fixed graph $F$. This is a natural extension of the study of regular graphs, and of the study of graphs of…
We prove some results concerning Alcuin number of graphs. First, we classify graphs which have unique minimum vertex cover. Then we present two necessary conditions for a graph to be of class two and show why one of them (condition on…
Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same…
List k-Coloring (Li k-Col) is the decision problem asking if a given graph admits a proper coloring compatible with a given list assignment to its vertices with colors in {1,2,..,k}. The problem is known to be NP-hard even for k=3 within…
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of…
We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of…
A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. In this paper, we first give a useful structural theorem for 1-planar graphs, and then apply it to the list edge and list total…
We consider the embeddability problem of a graph G into a two-dimensional simplicial complex C: Given G and C, decide whether G admits a topological embedding into C. The problem is NP-hard, even in the restricted case where C is…
Frick and Grohe [J. ACM 48 (2006), 1184-1206] introduced a notion of graph classes with locally bounded tree-width and established that every first order logic property can be decided in almost linear time in such a graph class. Here, we…
The distinguishing number of a graph $G$ is the smallest $k$ such that $G$ admits a $k$-colouring for which the only colour-preserving automorphism of $G$ is the identity. We determine the distinguishing number of finite $4$-valent…
An asymmetric coloring of a graph is a coloring of its vertices that is not preserved by any non-identity automorphism of the graph. The motion of a graph is the minimal degree of its automorphism group, i.e., the minimum number of elements…