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We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different…

Statistical Mechanics · Physics 2015-05-27 Alessandro Pelizzola , Marco Pretti , Jort van Mourik

Unsupervised plain graph alignment (UPGA) aims to align corresponding nodes across two graphs without any auxiliary information. Existing UPGA methods rely on structural consistency while neglecting the inherent structural differences in…

Social and Information Networks · Computer Science 2025-06-24 Boyan Wang , Weijie Feng , Jinyang Huang , Dan Guo , Zhi Liu

We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…

Discrete Mathematics · Computer Science 2012-11-06 Ajit Diwan , Soumitra Pal , Abhiram Ranade

Graph Coloring consists in assigning colors to vertices ensuring that two adjacent vertices do not have the same color. In dynamic graphs, this notion is not well defined, as we need to decide if different colors for adjacent vertices must…

Discrete Mathematics · Computer Science 2025-05-16 Allen Ibiapina , Minh Hang Nguyen , Mikaël Rabie , Cléophée Robin

The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…

Combinatorics · Mathematics 2026-02-16 Aida Abiad , Pax Mallee

This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the…

Machine Learning · Computer Science 2023-12-25 Todd Hildebrant

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color…

Graphics · Computer Science 2016-10-11 Shuang Zhao , Fredo Durand , Changxi Zheng

We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the…

Analysis of PDEs · Mathematics 2013-05-28 Xavier Blanc , Benjamin Edouard Peigney

Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…

Machine Learning · Computer Science 2024-11-05 Zhe Xu , Ruizhong Qiu , Yuzhong Chen , Huiyuan Chen , Xiran Fan , Menghai Pan , Zhichen Zeng , Mahashweta Das , Hanghang Tong

Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…

Discrete Mathematics · Computer Science 2023-05-17 Delia Garijo , Alberto Márquez , Rafael Robles

A circle graph is a graph in which the adjacency of vertices can be represented as the intersection of chords of a circle. The problem of calculating the chromatic number is known to be NP-complete, even on circle graphs. In this paper, we…

Discrete Mathematics · Computer Science 2025-09-25 Masato Tanaka , Tomomi Matsui

Graph coloring has been broadly used to discover concurrency in parallel computing. To speedup graph coloring for large-scale datasets, parallel algorithms have been proposed to leverage modern GPUs. Existing GPU implementations either have…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-01-22 Xuhao Chen , Pingfan Li , Jianbin Fang , Tao Tang , Zhiying Wang , Canqun Yang

Hypergraphs are important objects to model ternary or higher-order relations of objects, and have a number of applications in analysing many complex datasets occurring in practice. In this work we study a new heat diffusion process in…

Data Structures and Algorithms · Computer Science 2022-05-06 Peter Macgregor , He Sun

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…

Neural and Evolutionary Computing · Computer Science 2007-05-23 V. C. Barbosa , C. A. G. Assis , J. O. do Nascimento

Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of…

Combinatorics · Mathematics 2024-08-13 Andrea C. Burgess , John A. Hawkin , Alexander J. M. Howse , Caleb W. Jones , David A. Pike

We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…

Data Structures and Algorithms · Computer Science 2015-01-12 Tomomi Matsui , Noriyoshi Sukegawa , Atsushi Miyauchi

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…

Discrete Mathematics · Computer Science 2019-06-12 George B. Mertzios , Hendrik Molter , Viktor Zamaraev

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…

Statistical Mechanics · Physics 2009-11-11 S. Bounkong , J. van Mourik , D. Saad

Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…

We observe a network scenario where parts of a secret are distributed among its nodes. Within the network, a group of attackers is actively trying to obtain the complete secret, while there is also the issue of some nodes malfunctioning or…

Combinatorics · Mathematics 2023-10-10 Tanja Vojkovic , Damir Vukicevic