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Finding Large p-Colored Diameter Two Subgraphs
TLDR
It is shown for k≥1 and k\2≤p≤k that there is always a p-colored diameter two subgraph of Kn containing at least vertices and that this is best possible up to an additive constant l satisfying 0≤l.
The Specification of 2-trees
TLDR
New functional equations at a species level for certain classes of 2-trees, including a dissymmetry theorem are derived, including an theoreme of dissymetrie, which is more explicit than previously known results.
Finding Large Monochromatic Diameter Two Subgraphs
Given a coloring of the edges of the complete graph on n vertices in k colors, by considering the neighbors of an arbitrary vertex it follows that there is a monochromatic diameter two subgraph on at
Specifying 2-trees
We derive new functional equations at a species level for 2-trees including a new dissymmetry theorem. From these equations we deduce various enumerative series expansions for certain classes of