Related papers: Unary Automatic Graphs: An Algorithmic Perspective
We define pure graphs, invertible graphs, and the notion of complementation of bicoloured graphs. The study of pure graphs is motivated by two conjectures about the transition systems of eulerian graphs and by the Cycle Double Cover…
In this paper we study the realizability question for commuting graphs of finite groups: Given an undirected graph $X$ is it the commuting graph of a group $G$? And if so, to determine such a group. We seek efficient algorithms for this…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
Every countable graph can be built from finite graphs by a suitable infinite process, either adding new vertices randomly or imposing some rules on the new edges. On the other hand, a profinite topological graph is built as the inverse…
We show that any finitely dependent invariant process on a transitive amenable graph is a finitary factor of an i.i.d. process. With an additional assumption on the geometry of the graph, namely that no two balls with different centers are…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
A finite graph $\Gamma$ is called $G$-symmetric if $G$ is a group of automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma$. We study a family of symmetric graphs, called the unitary…
Strongly chordal graphs are a subclass of chordal graphs. The interest in this subclass stems from the fact that many problems which are NP-complete for chordal graphs are solvable in polynomial time for this subclass. However, we are not…
We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems…
In this paper, we introduce the notion of a finite non-simple directed graph, called an ornated graph and initiate a study on ornated graphs. An ornated graph is a directed graph on $n$ vertices, denoted by $O_n(s_l)$, whose vertices are…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
For each infinite word over a given finite alphabet, we define an increasing sequence of rooted finite graphs, that can be thought as approximations of the famous Sierpinski carpet. These sequences naturally converge to an infinite rooted…
We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not…
We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
A graph has the unique path property UPP_n if there is a unique path of length n between any ordered pair of nodes. This paper reiterates Royle and MacKay's technique for constructing orderly algorithms. We wish to use this technique to…
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be…
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…