Geodesic
The restricted arc-width of a graph
The electronic journal of combinatorics, Tome 10 (2003)
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An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Barát and Hajnal on this subject and develop a generalization we call restricted arc-width. Our main results revolve around using this to bound arc-width from below and to examine the effect of several graph operations on arc-width. In particular, we completely describe the effect of disjoint unions and wedge sums while providing tight bounds on the effect of cones.
DOI : 10.37236/1734
Classification : 05C62, 05C83 
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     author = {David Arthur},
     title = {The restricted arc-width of a graph},
     journal = {The electronic journal of combinatorics},
     year = {2003},
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     doi = {10.37236/1734},
     zbl = {1031.05088},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1734/}
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David Arthur. The restricted arc-width of a graph. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1734

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