Journal Article10.1145/3341.3350
A generalized implicit enumeration algorithm for graph coloring
Marek Kubale,Boguslaw Jackowski +1 more
127
TL;DR: A generalized algorithm for graph coloring by implicit enumeration is formulated and a number of backtracking sequential methods are discussed in terms of the generalized algorithm.
read more
Abstract: A generalized algorithm for graph coloring by implicit enumeration is formulated. A number of backtracking sequential methods are discussed in terms of the generalized algorithm. Some are revealed to be partially correct and inexact. A few corrections to the invalid algorithms, which cause these algorithms to guarantee optimal solutions, are proposed. Finally, some computational results and remarks on the practical relevance of improved implicit enumeration algorithms are given.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The maximum clique problem
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
1.1K
SNDlib 1.0—Survivable Network Design Library
TL;DR: The data concepts of SNDlib are discussed and a mathematical model for each design problem considered in the library is described, which leads to 830 network design problem instances.
Panconnectivity, fault-tolerant hamiltonicity and hamiltonian-connectivity in alternating group graphs
TL;DR: In this paper, the authors showed that all alternating group graphs are pan-connected, that is, every two vertices x and y in the graph are connected by a path of length k for each k satisfying dlx, yr ≤ k ≤ vVv - 1, where d lx, y denotes the distance between X and y, and vvv is the number of vertices in the network.
152
School timetable construction : algorithms and complexity
RJ Roy Willemen
- 01 Jan 2002
TL;DR: The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.
Design, Implementation, and Evaluation of the Constraint Language cc(FD)
Pascal Van Hentenryck,Vijay Saraswat,Yves Deville +2 more
- 16 May 1994
TL;DR: Results on numerous problems, including scheduling, resource allocation, sequencing, packing, and hamiltonian paths are reported, and indicate that cc(FD) comes close to procedural languages on a number of combinatorial problems.
References
Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.
2.4K
New methods to color the vertices of a graph
TL;DR: An exact method is given which performs better than the Randall-Brown algorithm and is able to color larger graphs and the new heuristic methods, the classical methods, and the exact method are compared.
1.7K
Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete
TL;DR: It is shown that two sorts of problems belong to the NP-complete class, and a result by Garey, Johnson, and Stockmeyer is extended with a proof that the coloring of four-regular planar graphs is NP- complete.
196