Characterization of $[1,k]$-Bar Visibility Trees
نویسندگان
چکیده
منابع مشابه
Characterization of [1, k]-Bar Visibility Trees
A unit bar-visibility graph is a graph whose vertices can be represented in the plane by disjoint horizontal unit-length bars such that two vertices are adjacent if and only if there is a unobstructed, non-degenerate, vertical band of visibility between the corresponding bars. We generalize unit bar-visibility graphs to [1, k]bar-visibility graphs by allowing the lengths of the bars to be betwe...
متن کاملBAR k-VISIBILITY GRAPHS
Die selbständige und eigenhändige Anfertigung versichere ich an Eides statt. Conclusion 71 Bibliography 75 Introduction " The true mystery of the world is the visible, not the invisible. " Oscar Wilde How can geometric settings be encoded combinatorially? Which discrete structures extract the essential information from continuous arrangements? How can the combinatorial properties of visibility ...
متن کاملBar k-Visibility Graphs
Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one correspondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. If bars are a...
متن کاملThickness of Bar 1-Visibility Graphs
Bar k-visibility graphs are graphs admitting a representation in which the vertices correspond to horizontal line segments, called bars, and the edges correspond to vertical lines of sight which can traverse up to k bars. These graphs were introduced by Dean et al. [3] who conjectured that bar 1-visibility graphs have thickness at most 2. We construct a bar 1-visibility graph having thickness 3...
متن کاملParameters of Bar k-Visibility Graphs
Bar k-visibility graphs are graphs admitting a representation in which the vertices correspond to horizontal line segments, called bars, and the edges correspond to vertical lines of sight which can traverse up to k bars. These graphs were introduced by Dean et al. [4] who conjectured that bar 1-visibility graphs have thickness at most 2. We construct a bar 1-visibility graph having thickness 3...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2006
ISSN: 1077-8926
DOI: 10.37236/1116