相关论文: An experimental approach: The graph of graphs

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…

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…

In graph coloring problems, the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic graph coloring, the goal is to minimize the…

This paper is concerned with efficiently coloring sparse graphs in the distributed setting with as few colors as possible. According to the celebrated Four Color Theorem, planar graphs can be colored with at most 4 colors, and the proof…

Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…

The design of a good algorithm to solve NP-hard combinatorial approximation problems requires specific domain knowledge about the problems and often needs a trial-and-error problem solving approach. Graph coloring is one of the essential…

Proper graph coloring assigns different colors to adjacent vertices of the graph. Usually, the number of colors is fixed or as small as possible. Consider applications (e.g. variants of scheduling) where colors represent limited resources…

Shape is commonly used to distinguish between categories in multi-class scatterplots. However, existing guidelines for choosing effective shape palettes rely largely on intuition and do not consider how these needs may change as the number…

Let $G$ be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of $k$ colors. For two given list colorings of $G$, we study the problem of transforming one into…

Recent advancements in retrieval-augmented generation (RAG) have enhanced large language models in question answering by integrating external knowledge. However, challenges persist in achieving global understanding and aligning responses…

A proper coloring of a graph is \emph{conflict-free} if, for every non-isolated vertex, some color is used exactly once on its neighborhood. Caro, Petru\v{s}evski, and \v{S}krekovski proved that every graph $G$ has a proper conflict-free…

A path in an edge-colored graph is called a proper path if no two adjacent edges of the path receive the same color. For a connected graph $G$, the proper connection number $pc(G)$ of $G$ is defined as the minimum number of colors needed to…

The quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful…

In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…

We consider the subgraph isomorphism problem where, given two graphs G (source graph) and F (pattern graph), one is to decide whether there is a (not necessarily induced) subgraph of G isomorphic to F. While many practical heuristic…

Many circumstances of practical importance have performance or success metrics which exist implicitly---in the eye of the beholder, so to speak. Tuning aspects of such problems requires working without defined metrics and only considering…

Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…

In this paper, we consider a number of results and seven conjectures on properly edge-coloured (PC) paths and cycles in edge-coloured multigraphs. We overview some known results and prove new ones. In particular, we consider a family of…

This study proposes a tactile diagram pattern for visually impaired people to recognize color information. The pattern uses the principle of three primary colors, with different patterns representing red, blue, and yellow. The size of…

We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the…