The cyclic coloring problem and estimation of spare hessian matrices
SIAM Journal on Algebraic and Discrete Methods
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Minimum feedback vertex set and acyclic coloring
Information Processing Letters
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Acyclic and k-distance coloring of the grid
Information Processing Letters
Acyclic colorings of products of trees
Information Processing Letters
Acyclic coloring of graphs of maximum degree five: Nine colors are enough
Information Processing Letters
A cutting plane algorithm for graph coloring
Discrete Applied Mathematics
New Acyclic and Star Coloring Algorithms with Application to Computing Hessians
SIAM Journal on Scientific Computing
Acyclic list 7-coloring of planar graphs
Journal of Graph Theory
On the acyclic choosability of graphs
Journal of Graph Theory
Acyclic 5-choosability of planar graphs without small cycles
Journal of Graph Theory
On the Acyclic Chromatic Number of Hamming Graphs
Graphs and Combinatorics
Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation
INFORMS Journal on Computing
A Branch-and-Cut algorithm for graph coloring
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Random Structures & Algorithms
Cycle-based facets of chromatic scheduling polytopes
Discrete Optimization
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A coloring of a graph G is an assignment of colors to the vertices of G such that any two vertices receive distinct colors whenever they are adjacent. An acyclic coloring of G is a coloring such that no cycle of G receives exactly two colors, and the acyclic chromatic number@g"A(G) of a graph G is the minimum number of colors in any such coloring of G. Given a graph G and an integer k, determining whether @g"A(G)@?k or not is NP-complete even for k=3. The acyclic coloring problem arises in the context of efficient computations of sparse and symmetric Hessian matrices via substitution methods. In this work we start an integer programming approach for this problem, by introducing a natural integer programming formulation and presenting six families of facet-inducing valid inequalities.