Author
David R. Guichard
Bio: David R. Guichard is an academic researcher from Whitman College. The author has contributed to research in topics: Mathematics & Cubic graph. The author has an hindex of 6, co-authored 11 publications receiving 184 citations.
Papers
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TL;DR: The maximum number of maximal independent sets which a connected graph on n vertices can have is determined, and the extremal graphs are completely characterize, thereby answering a question of Wilf.
92 citations
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TL;DR: It is shown that χ* < χ if and only if a particular digraph is acyclic and that the decisioin problem associated with this question is probably not in NP though it is both NP-hard and NP-easy.
Abstract: Star chromatic number, introduced by A. Vince, is a natural generalization of chromatic number. We consider the question, “When is χ* < χ?” We show that χ* < χ if and only if a particular digraph is acyclic and that the decisioin problem associated with this question is probably not in NP though it is both NP-hard and NP-easy. © 1993 John Wiley & Sons, Inc.
49 citations
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TL;DR: Which graphs containing no isolated vertices are domination graphs of tournaments are determined in this paper.
Abstract: A tournament is an oriented complete graph. Vertices x and y dominate a tournament T if for all vertices z≠x,y, either (x,z) or (y,z) are arcs in T (possibly both). The domination graph of a tournament T is the graph on the vertex set of T containing edge {x,y} if and only if x and y dominate T. In this paper we determine which graphs containing no isolated vertices are domination graphs of tournaments.
17 citations
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12 citations
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TL;DR: Two main theorems are proved that if a 1,…, a m are residues modulo n and m ⩾ n then some sum a i 1 + ⋯ + a ik , i 1 i k , is 0 (mod n).
8 citations
Cited by
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17 Dec 1994
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
Abstract: Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.
1,380 citations
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TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].
1,065 citations
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14 Jun 2009TL;DR: This work incorporates domain knowledge about the composition of words that should have high or low probability in various topics using a novel Dirichlet Forest prior in a LatentDirichlet Allocation framework.
Abstract: Users of topic modeling methods often have knowledge about the composition of words that should have high or low probability in various topics. We incorporate such domain knowledge using a novel Dirichlet Forest prior in a Latent Dirichlet Allocation framework. The prior is a mixture of Dirichlet tree distributions with special structures. We present its construction, and inference via collapsed Gibbs sampling. Experiments on synthetic and real datasets demonstrate our model's ability to follow and generalize beyond user-specified domain knowledge.
436 citations
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109 citations
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01 Jan 1998TL;DR: In this article, an arbitrary undirected graph without loops is defined as a graph where V = {v 1, v 2,…, v n } is its vertex set and E = {e 1,e 2, e m } ⊂ (E ×E) is its edge set.
Abstract: In this chapter G = (V,E) denotes an arbitrary undirected graph without loops, where V = {v 1, v 2,…, v n } is its vertex set and E = {e 1,e 2,…, e m } ⊂ (E ×E) is its edge set. Two edges are adjacent if they connect to a common vertex. Two vertices v i and v j are adjacent if there is an edge e = (v i ,v j ) ∈ E. Finally, if e = (v i ,v j ) ∈ E,we say e is incident to vertices v i , v j .
101 citations