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The restricted arc-width of a graph. (English) Zbl 1031.05088

Electron. J. Comb. 10, Research paper R41, 13 p. (2003); printed version J. Comb. 10, No. 4 (2003).
Summary: 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 J. Barát and P. Hajnal [Electron. J. Comb. 8, Research paper R34 (2001; Zbl 0996.05107)] 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.

MSC:

05C62 Graph representations (geometric and intersection representations, etc.)
05C83 Graph minors

Citations:

Zbl 0996.05107
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