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Kathie Cameron

Bio: Kathie Cameron is an academic researcher from Wilfrid Laurier University. The author has contributed to research in topics: Chordal graph & Split graph. The author has an hindex of 15, co-authored 49 publications receiving 729 citations.

Papers
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Journal ArticleDOI
TL;DR: It is shown that a maximum induced matching in a weakly chordal graph can be found in polynomial time and this generalizes previously known results for the induced matching problem.

105 citations

Journal ArticleDOI
TL;DR: It is shown that if G is a polygon-circle graph, then so is [ L ( G )] 2 , and the same holds for asteroidal triple-free and interval-filament graphs, and it follows that the induced matching problem is polytime-solvable in these classes.

89 citations

Journal ArticleDOI
TL;DR: This work gives a simple characterization of graphs and provides a simpler recognition algorithm for finding a maximum induced matching in a graph where equality holds.

61 citations

Journal ArticleDOI

60 citations

Journal ArticleDOI
TL;DR: It is shown that packing a maximum number of independent triangles is polynomial-time solvable for many classes of structured graphs, including weakly chordal graphs, asteroidal triple-free graphs, polygon-circle graphs, and interval-filament graphs.
Abstract: Packing a maximum number of disjoint triangles into a given graph G is NP-hard, even for most classes of structured graphs. In contrast, we show that packing a maximum number of independent (that is, disjoint and nonadjacent) triangles is polynomial-time solvable for many classes of structured graphs, including weakly chordal graphs, asteroidal triple-free graphs, polygon-circle graphs, and interval-filament graphs. These classes contain other well-known classes such as chordal graphs, cocomparability graphs, circle graphs, circular-arc graphs, and outerplanar graphs. Our results apply more generally to independent packings by members of any family of connected graphs.

51 citations


Cited by
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Journal ArticleDOI
16 Nov 2002
TL;DR: This work gives the first polynomial time algorithm to learn any function of a constant number of halfspaces under the uniform distribution to within any constant error parameter.
Abstract: We give the first polynomial time algorithm to learn any function of a constant number of halfspaces under the uniform distribution to within any constant error parameter. We also give the first quasipolynomial time algorithm for learning any function of a polylog number of polynomial-weight halfspaces under any distribution. As special cases of these results we obtain algorithms for learning intersections and thresholds of halfspaces. Our uniform distribution learning algorithms involve a novel non-geometric approach to learning halfspaces; we use Fourier techniques together with a careful analysis of the noise sensitivity of functions of halfspaces. Our algorithms for learning under any distribution use techniques from real approximation theory to construct low degree polynomial threshold functions.

197 citations

Journal ArticleDOI
TL;DR: In this work, Ramsey-type results concerning rainbow edge colorings of graphs are collected.
Abstract: In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.

176 citations

Dissertation
03 Sep 2012
TL;DR: The notion of branch decompositions of a set function introduced by Robert-son and Seymour is used to introduce three new graph parameters, boolean-width, max-imum matching-width (MM-width) and maximum induced matching- width (MIM-width), which are compared to existing graph parameters by comparing partial orders of width parameters.
Abstract: The main focus of this thesis is on using the divide and conquer technique toeciently solve graph problems that are in general intractable. We work inthe eld of parameterized algorithms, using width parameters of graphs thatindicate the complexity inherent in the structure of the input graph. We usethe notion of branch decompositions of a set function introduced by Robert-son and Seymour to de ne three new graph parameters, boolean-width, max-imum matching-width (MM-width) and maximum induced matching-width(MIM-width). We compare these new graph width parameters to existinggraph parameters by de ning partial orders of width parameters. We focuson tree-width, branch-width, clique-width, module-width and rank-width,and include a Hasse diagram of these orders containing 32 graph parameters.We use the size of a maximum matching in a bipartite graph as a setfunction to de ne MM-width and show that MM-width never di ers by morethan a multiplicative factor 3 from tree-width. The main reason for introduc-ing MM-width is that it simpli es the comparison between tree-width andparameters de ned via branch decomposition of a set function.We use the logarithm of the number of maximal independent sets in a bi-partite graph as set function to de ne boolean-width. We show that boolean-width of a graph class is bounded if and only if rank-width is bounded, andshow that the boolean-width of a graph can be as low as the logarithm of therank-width of the graph. Given a decomposition of boolean-width k, we de-sign FPT algorithms parameterized by k, for a large class of graph problems,whose runtime has a single exponential dependency in the boolean-width,i.e. O

144 citations

Journal IssueDOI
TL;DR: In this article, the existence of monochromatic spanning trees in complete graphs with no tricolored triangles was shown to be a special case of edge colorings of complete graphs.
Abstract: We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and Voxman about the existence of special monochromatic spanning trees in such colorings. We also determine the size of largest monochromatic stars guaranteed to occur. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 211–216, 2004

138 citations

Journal ArticleDOI
TL;DR: It is shown some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles and two conjectures of Bialostocki and Voxman about the existence of special monochromatic spanning trees in such colorings are proved.
Abstract: We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and Voxman about the existence of special monochromatic spanning trees in such colorings. We also determine the size of largest monochromatic stars guaranteed to occur. 2004 Wiley Periodicals, Inc. J Graph Theory 46: 211–216, 2004

130 citations