Applied combinatorics
Coloring perfect (K4-e)-free graphs
Journal of Combinatorial Theory Series B
Convergence of iterated clique graphs
Discrete Mathematics
Kernels in perfect line-graphs
Journal of Combinatorial Theory Series B
The list chromatic index of a bipartite multigraph
Journal of Combinatorial Theory Series B
Bipartite Edge Coloring in $O(\Delta m)$ Time
SIAM Journal on Computing
Sequential colorings and perfect graphs
Proceedings of the third international conference on Graphs and optimization
Perfect Constraints Are Tractable
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
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Gridline graphs can be realized in the plane with vertices adjacent whenever they are on a common vertical or horizontal line. We review some applications and characterizations, e.g. they are line graphs of bipartite graphs, and provide practical O(|V|3) algorithms for some classical problems. We extend gridline graphs from the plane to higher dimensions. We characterize these graphs using a vertex coloring of the clique graph that corresponds to the conditions that, in the intersection graph of lines parallel to axes in Rn, any cycle of four lines must remain in two dimensions and any path between two given lines must traverse the same two dimensions.