GRAPH COLORING ALGORITHMS††This research was supported in part by the Advanced Research Projects Agency of the Department of Defense under contract SD-302 and by the National Science Foundation under contract GJ-446.

Matula, David W.; Marble, George; Isaacson, Joel D.

doi:10.1016/b978-1-4832-3187-7.50015-5

Cited by 155 publications

(18 citation statements)

References 8 publications

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“…Both Matula and Szekeres and Wilf have methods for determining the value of the width analog for a given graph and for obtaining a corresponding ordering of the vertices and a coloring within the established bound. These results are summarized in [9], where a concept of "sequential coloring" is described which is essentially equivalent to a backtrack-free vertical search order in the graph coloring context. This paper serves to generalize this graph coloring work to the larger context of constraint satisfaction (although as it happens my work arose from concerns with constraints and backtracking, and I only belatedly became aware of these related developments in graph theory).…”

Section: Graph Theory Connectionsmentioning

confidence: 99%

A Sufficient Condition for Backtrack-Free Search

Freuder

1982

J. ACM

491

208

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ABSTRACT. A constraint satisfaction problem revolves finding values for a set of variables subject to a set of constraints (relations) on those variables Backtrack search is often used to solve such problems. A relationship involving the structure of the constraints is described which characterizes to some degree the extreme case of mimmum backtracking (none) The relationship involves a concept called "width," which may provide some guidance in the representation of constraint satisfaction problems and the order m which they are searched The width concept is studied and applied, in particular, to constraints which form tree structures.

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Section: Graph Theory Connectionsmentioning

confidence: 99%

A Sufficient Condition for Backtrack-Free Search

Freuder

1982

J. ACM

491

208

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“…Elles s'appuyent sur des considérations heuristiques. La qualité des estimations du nombre chromatique qu'elles donnent dépend de la structure du graphe (Matula [9], Thérani [13]). …”

Section: Introductionunclassified

Note sur une application de la classification hiérarchique à la coloration des graphes

Thépot¹,

Lechenault²

1981

RAIRO-Oper. Res.

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“…[22,23,24]). The proposed exact algorithms mostly used some form of backtrack search to guarantee a complete search while also being able to prune potentially large parts of the search space.…”

Section: Previous Workmentioning

confidence: 99%

Average-case complexity of backtrack search for coloring sparse random graphs

Mann

Szajkó

2013

Journal of Computer and System Sciences

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We investigate asymptotically the expected number of steps taken by backtrack search for k-coloring random graphs G n,p(n) or proving non-k-colorability, where p(n) is an arbitrary sequence tending to 0, and k is constant. Contrary to the case of constant p, where the expected runtime is known to be O(1), we prove that here the expected runtime tends to infinity. We establish how the asymptotic behaviour of the expected number of steps depends on the sequence p(n). In particular, for p(n) = d/n, where d is a constant, the runtime is always exponential, but it can be also polynomial if p(n) decreases sufficiently slowly, e.g. for p(n) = 1/ ln n.

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GRAPH COLORING ALGORITHMS††This research was supported in part by the Advanced Research Projects Agency of the Department of Defense under contract SD-302 and by the National Science Foundation under contract GJ-446.

Cited by 155 publications

References 8 publications

A Sufficient Condition for Backtrack-Free Search

A Sufficient Condition for Backtrack-Free Search

Note sur une application de la classification hiérarchique à la coloration des graphes

Average-case complexity of backtrack search for coloring sparse random graphs

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