Coloring Artemis graphs

We consider the class A of graphs that contain no odd hole, no antihole, and no ``prism'' (a graph consisting of two disjoint triangles with three disjoint paths between them). We show that the coloring algorithm found by the second and fourth author can be implemented in time O(n^2m) for any graph in A with n vertices and m edges, thereby improving on the complexity proposed in the original paper

On characterizing game-perfect graphs by forbidden induced subgraphs

A graph $G$ is called $g$-perfect if, for any induced subgraph $H$ of $G$, the game chromatic number of $H$ equals the clique number of $H$. A graph $G$ is called $g$-col-perfect if, for any induced subgraph $H$ of $G$, the game coloring number of $H$ equals the clique number of $H$. In this paper we characterize the classes of $g$-perfect resp. $g$-col-perfect graphs by a set of forbidden induced subgraphs and explicitly. Moreover, we study similar notions for variants of the game chromatic number, namely $B$-perfect and $[A,B]$-perfect graphs, and for several variants of the game coloring number, and characterize the classes of these graphs

Paperfolding morphisms, planefilling curves, and fractal tiles

An interesting class of automatic sequences emerges from iterated paperfolding. The sequences generate curves in the plane with an almost periodic structure. We generalize the results obtained by Davis and Knuth on the self-avoiding and planefilling properties of these curves, giving simple geometric criteria for a complete classification. Finally, we show how the automatic structure of the sequences leads to self-similarity of the curves, which turns the planefilling curves in a scaling limit into fractal tiles. For some of these tiles we give a particularly simple formula for the Hausdorff dimension of their boundary.Comment: 32 pages, 23 figure