Displaying similar documents to “The lattice of threshold graphs.”

Sum of squares of degrees in a graph.

Ábrego, Bernardo M., Fernández-Merchant, Silvia, Neubauer, Michael G., Watkins, William (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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Spatially-distributed coverage optimization and control with limited-range interactions

Jorge Cortés, Sonia Martínez, Francesco Bullo (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed...

Star Coloring of Subcubic Graphs

T. Karthick, C.R. Subramanian (2013)

Discussiones Mathematicae Graph Theory

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A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.