相关论文: A corrected strategy for proving no finite variabl…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that…

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…

We prove the celebrated representation theorem of Andreka-Resek-Thompson, together with its polyadic analogue by Ferenczi, using games as introduced in algebraic logic by Hirsch and Hodkinson. We also show that atomic algebras are…

This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…

Conventional Ramsey-theoretic investigations for edge-colourings of complete graphs are framed around avoidance of certain configurations. Motivated by considerations arising in the field of Qualitative Reasoning, we explore edge colourings…

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…

Let $X$ be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring $\phi\colon X\to\{0,1\}$ and some $R\in\mathbb{N}$ such that every automorphism $f$ preserving $\phi$ is $R$-close to the identity…

A homomorphism from a graph $X$ to a graph $Y$ is an adjacency preserving mapping $f:V(X) \rightarrow V(Y)$. We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph $X$ admits a…

Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…

We show that the edges of every 3-connected planar graph except $K_4$ can be colored with two colors in such a way that the graph has no color preserving automorphisms. Also, we characterize all graphs which have the property that their…

Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.

In this paper, we first study a new extremal problem recently posed by Conlon and Tyomkyn~(arXiv: 2002.00921). Given a graph $H$ and an integer $k\geqslant 2$, let $f_{k}(n,H)$ be the smallest number of colors $c$ such that there exists a…

Let $W$ be a Coxeter group whose proper parabolic subgroups are finite. According to Theorem~1.12 of [1], if the module of a finite $W$-digraph $\Gamma$ is isomorphic to the module of a $W$-graph over $Q$, then $\Gamma$ is acyclic. We…

We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

We describe a general method for constructing representations of finite integral symmetric relation algebras from distance-regular graphs. Given a distance-regular graph of diameter $d$, the distances between vertices induces a coloring of…

Recently, connections have been explored between the complexity of finite problems in graph theory and the complexity of their infinite counterparts. As is shown in our paper (and in independent work of Tirza Hirst and D. Harel from a…

We study turn-based quantitative games of infinite duration opposing two antagonistic players and played over graphs. This model is widely accepted as providing the adequate framework for formalizing the synthesis question for reactive…

We prove a new generalisation of Ramsey's theorem by showing that every $2$-edge-coloured graph with sufficiently large minimum degree contains a monochromatic induced subgraph whose minimum degree remains large. From this, we also derive…