Paths in interval graphs and circular arc graphs

Longest Paths in Circular Arc Graphs

We show that all maximum length paths in a connected circular arc graph have non–empty intersection.

Interval Routing Schemes for Circular-Arc Graphs

Interval routing is a space efficient method to realize a distributed routing function. In this paper we show that every circular-arc graph allows a shortest path strict 2-interval routing scheme, i.e., by introducing a global order on the vertices and assigning at most two (strict) intervals in this order to the ends of every edge allows to depict a routing function that implies exclusively sh...

Induced Disjoint Paths in Circular-Arc Graphs in Linear Time

The Induced Disjoint Paths problem is to test whether an graph G on n vertices with k distinct pairs of vertices (si, ti) contains paths P1, . . . , Pk such that Pi connects si and ti for i = 1, . . . , k, and Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their ends) for 1 ≤ i < j ≤ k. We present a linear-time algorithm that solves Induced Disjoint Paths and finds...

Bipartite probe interval graphs, circular arc graphs, and interval point bigraphs

A Note on Longest Paths in Circular Arc Graphs

As observed by Rautenbach and Sereni [SIAM J. Discrete Math. 28 (2014) 335–341] there is a gap in the proof of the theorem of Balister et al. [Combin. Probab. Comput. 13 (2004) 311–317], which states that the intersection of all longest paths in a connected circular arc graph is nonempty. In this paper we close this gap.