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We study the problem of coloring a given graph using a small number of colors in several well-established models of computation for big data. These include the data streaming model, the general graph query model, the massively parallel…

Data Structures and Algorithms · Computer Science 2019-05-03 Suman K. Bera , Amit Chakrabarti , Prantar Ghosh

A $k$-coloring of a graph is an assignment of integers between $1$ and $k$ to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further…

Combinatorics · Mathematics 2018-09-24 Jie You , Yixin Cao , Jianxin Wang

We analyze the computational complexity of the following computational problems called Bounded-Density Edge Deletion and Bounded-Density Vertex Deletion: Given a graph $G$, a budget $k$ and a target density $\tau_\rho$, are there $k$ edges…

Data Structures and Algorithms · Computer Science 2024-04-15 Cristina Bazgan , André Nichterlein , Sofia Vazquez Alferez

An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs. Recall that the…

Discrete Mathematics · Computer Science 2024-02-14 Hanna Furmańczyk , Vahan Mkrtchyan

Coloring is used in wireless networks to improve communication efficiency, mainly in terms of bandwidth, energy and possibly end-to-end delays. In this research report, we define the h-hop node coloring problem, with h any positive integer.…

Networking and Internet Architecture · Computer Science 2011-04-12 Ichrak Amdouni , Pascale Minet , Cédric Adjih

We study the NP-hard Fair Connected Districting problem recently proposed by Stoica et al. [AAMAS 2020]: Partition a vertex-colored graph into k connected components (subsequently referred to as districts) so that in every district the most…

Computer Science and Game Theory · Computer Science 2022-04-11 Niclas Boehmer , Tomohiro Koana , Rolf Niedermeier

In this paper, we study the Target Set Selection problem from a parameterized complexity perspective. Here for a given graph and a threshold for each vertex, the task is to find a set of vertices (called a target set) which activates the…

Data Structures and Algorithms · Computer Science 2020-08-17 Pavel Dvořák , Dušan Knop , Tomáš Toufar

We study the parameterized complexity of the T(h+1)-Free Edge Deletion problem. Given a graph G and integers k and h, the task is to delete at most k edges so that every connected component of the resulting graph has size at most h. The…

Data Structures and Algorithms · Computer Science 2026-02-04 Ajinkya Gaikwad , Soumen Maity , Leeja R

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a…

Computational Complexity · Computer Science 2017-03-21 Yijia Chen , Martin Grohe , Bingkai Lin

In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…

Quantum Physics · Physics 2024-08-08 Tatsuya Terao , Ryuhei Mori

We introduce the Multicolored Graph Realization problem (MGRP). The input to the problem is a colored graph $(G,\varphi)$, i.e., a graph together with a coloring on its vertices. We can associate to each colored graph a cluster graph…

Computational Complexity · Computer Science 2021-03-25 Josep Díaz , Öznur Yaşar Diner , Maria Serna , Oriol Serra

Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology \cite{Civan}, and the framework through which it was studied, we introduce the linear coloring on graphs. We…

Discrete Mathematics · Computer Science 2008-07-29 Kyriaki Ioannidou , Stavros D. Nikolopoulos

The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs…

Data Structures and Algorithms · Computer Science 2020-09-29 Thomas Bellitto , Shaohua Li , Karolina Okrasa , Marcin Pilipczuk , Manuel Sorge

We consider the single-conflict coloring problem, a graph coloring problem in which each edge of a graph receives a forbidden ordered color pair. The task is to find a vertex coloring such that no two adjacent vertices receive a pair of…

Combinatorics · Mathematics 2026-03-16 Peter Bradshaw , Tomáš Masařík

The generalized coloring numbers of Kierstead and Yang (Order 2003) offer an algorithmically-useful characterization of graph classes with bounded expansion. In this work, we consider the hardness and approximability of these parameters.…

Computational Complexity · Computer Science 2023-03-17 Michael Breen-McKay , Brian Lavallee , Blair D. Sullivan

The Weisfeiler-Leman dimension of a graph $G$ is the least number $k$ such that the $k$-dimensional Weisfeiler-Leman algorithm distinguishes $G$ from every other non-isomorphic graph. The dimension is a standard measure of the descriptive…

Computational Complexity · Computer Science 2024-11-18 Moritz Lichter , Simon Raßmann , Pascal Schweitzer

We investigate the parameterized complexity of Maximum Exposure Problem (MEP). Given a range space (R, P) where R is the set of ranges containing a set P of points, and an integer k, MEP asks for k ranges which on removal results in the…

Computational Geometry · Computer Science 2022-03-23 Remi Raman , Shahin John J S , R Subashini , Subhasree Methirumangalath

We study the well-known Vertex Cover problem parameterized above and below tight bounds. We show that two of the parameterizations (both were suggested by Mahajan, Raman and Sikdar, J. Computer and System Sciences, 75(2):137--153, 2009) are…

Computational Complexity · Computer Science 2009-08-28 Gregory Gutin , Eun Jung Kim , Michael Lampis , Valia Mitsou

A $(p,q)$-coloring of a graph $G$ is an edge-coloring of $G$ which assigns at least $q$ colors to each $p$-clique. The problem of determining the minimum number of colors, $f(n,p,q)$, needed to give a $(p,q)$-coloring of the complete graph…

Combinatorics · Mathematics 2020-06-23 Alex Cameron , Emily Heath

Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…

Combinatorics · Mathematics 2025-06-10 Charles Burnette , Broden Caton , Olivia Coward , Julian Davis , Austin Teter