0000000000557463

AUTHOR

Brice Effantin

showing 3 related works from this author

The b-chromatic number of power graphs

2003

The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x_i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.

b-chromatic numberGeneral Computer Science[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]power graphTheoretical Computer ScienceCombinatoricsComputer Science::Discrete MathematicsDiscrete Mathematics and CombinatoricsChromatic scaleGraph coloringcoloringMathematicscycle and complete binary treeMathematics::CombinatoricsBinary treelcsh:Mathematicscycle and complete binary tree.path[ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM]Complete coloringlcsh:QA1-939Vertex (geometry)Brooks' theorem[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Edge coloringFractional coloringDiscrete Mathematics & Theoretical Computer Science
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Generation of Valid Labeled Binary Trees

2003

International audience; Generating binary trees is a well-known problem. In this paper, we add some constraints to leaves of these trees. Such trees are used in the morphing of polygons, where a polygon P is represented by a binary tree T and each angle of P is a weight on a leaf of T. In the following, we give two algorithms to generate all binary trees, without repetitions, having the same weight distribution to their leaves and representing all parallel polygons to P.

Discrete mathematicsBinary treeOptimal binary search tree[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Weight-balanced tree[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]Scapegoat treeComputer Science::Computational GeometryRandom binary treeCombinatoricsBinary search treeTernary search treeMetric treeMathematicsComputingMethodologies_COMPUTERGRAPHICS
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On parameterized complexity to determine b-chromatic and partial Grundy numbers

2014

International audience

[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO][MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO][INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS][INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]ComputingMilieux_MISCELLANEOUS
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