Geodesic
The arc-width of a graph
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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The arc-representation of a graph is a mapping from the set of vertices to the arcs of a circle such that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs having a point in common. The arc-width ($aw$) of a graph is the minimum width of its arc-representations. We show how arc-width is related to path-width and vortex-width. We prove that $aw(K_{s,s})=s$.
DOI : 10.37236/1578
Classification : 05C83, 05C62
Mots-clés : arc-represention 
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     author = {J\'anos Bar\'at and P\'eter Hajnal},
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János Barát; Péter Hajnal. The arc-width of a graph. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1578

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