
Number of Cliques in Minor-Closed Classes ★★
Author(s): Wood




A gold-grabbing game ★★
Author(s): Rosenfeld
Setup Fix a tree and for every vertex
a non-negative integer
which we think of as the amount of gold at
.
2-Player game Players alternate turns. On each turn, a player chooses a leaf vertex of the tree, takes the gold at this vertex, and then deletes
. The game ends when the tree is empty, and the winner is the player who has accumulated the most gold.
Crossing numbers and coloring ★★★
Author(s): Albertson
We let denote the crossing number of a graph
.



Keywords: coloring; complete graph; crossing number
Domination in cubic graphs ★★
Author(s): Reed


Keywords: cubic graph; domination
Do filters complementive to a given filter form a complete lattice? ★★
Author(s): Porton
Let is a set. A filter (on
)
is by definition a non-empty set of subsets of
such that
. Note that unlike some other authors I do not require
. I will denote
the lattice of all filters (on
) ordered by set inclusion.
Let is some (fixed) filter. Let
. Obviously
is a bounded lattice.
I will call complementive such filters that:
;
is a complemented element of the lattice
.
Keywords: complete lattice; filter