
Cycle Intersection Graphs and Minimum Decycling Sets of Even Graphs
We introduce the cycle intersection graph of a graph, an adaptation of t...
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Random 2cell embeddings of multistars
By using permutation representations of maps, one obtains a bijection be...
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Lazy Search Trees
We introduce the lazy search tree data structure. The lazy search tree i...
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On graphs with no induced fivevertex path or paraglider
Given two graphs H_1 and H_2, a graph is (H_1, H_2)free if it contains ...
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An Upper Bound for Sorting R_n with LRE
A permutation π over alphabet Σ = 1,2,3,...,n, is a sequence where every...
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Faster 3coloring of smalldiameter graphs
We study the 3Coloring problem in graphs with small diameter. In 2013, ...
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Oriented Diameter of Star Graphs
An orientation of an undirected graph G is an assignment of exactly one...
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Dynamic Schnyder Woods
A realizer, commonly known as Schnyder woods, of a triangulation is a partition of its interior edges into three oriented rooted trees. A flip in a realizer is a local operation that transforms one realizer into another. Two types of flips in a realizer have been introduced: colored flips and cycle flips. A corresponding flip graph is defined for each of these two types of flips. The vertex sets are the realizers, and two realizers are adjacent if they can be transformed into each other by one flip. In this paper we study the relation between these two types of flips and their corresponding flip graphs. We show that a cycle flip can be obtained from linearly many colored flips. We also prove an upper bound of O(n^2) on the diameter of the flip graph of realizers defined by colored flips. In addition, a data structure is given to dynamically maintain a realizer over a sequence of colored flips which supports queries, including getting a node's barycentric coordinates, in O(log n) time per flip or query.
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