Simultaneous graph drawing: layout algorithms and visualization schemes.
Some news about oblique graphs
A k-gon α of a polyhedral graph G(V,E,F) is of type ⟨b₁,b₂,...,bₖ⟩ if the vertices incident with α in cyclic order have degrees b₁,b₂,...,bₖ and ⟨b₁,b₂,...,bₖ⟩ is the lexicographic minimum of all such sequences available for α. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3.
Some Variations of Perfect Graphs
We consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) = γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k-path vertex cover number and the distance (k − 1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k ≥ 2. Moreover, we provide a complete characterisation of (ψ2 − γ1)- perfect graphs describing the set of its forbidden induced subgraphs and providing the explicit characterisation of the structure of graphs belonging...
Spatial graphs, knots and the cyclic polytope.
Splitting Cubic Circle Graphs
We show that every 3-regular circle graph has at least two pairs of twin vertices; consequently no such graph is prime with respect to the split decomposition. We also deduce that up to isomorphism, K4 and K3,3 are the only 3-connected, 3-regular circle graphs.
Stacks, queues and tracks: layouts of graph subdivisions.
Straight-line drawings of binary trees with linear area and arbitrary aspect ratio.
Straight-line drawings on restricted integer grids in two and three dimensions.
Strictly convex drawings of planar graphs.
Strongly pancyclic and dual-pancyclic graphs
Say that a cycle C almost contains a cycle C¯ if every edge except one of C¯ is an edge of C. Call a graph G strongly pancyclic if every nontriangular cycle C almost contains another cycle C¯ and every nonspanning cycle C is almost contained in another cycle C⁺. This is equivalent to requiring, in addition, that the sizes of C¯ and C⁺ differ by one from the size of C. Strongly pancyclic graphs are pancyclic and chordal, and their cycles enjoy certain interpolation and extrapolation properties with...
Symmetry of iteration graphs
We examine iteration graphs of the squaring function on the rings when , for a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when and when and are symmetric when .