
Triangle free strongly regular graphs ★★★
Author(s):
Problem Is there an eighth triangle free strongly regular graph?
Keywords: strongly regular; triangle free
Alon-Saks-Seymour Conjecture ★★★
Author(s): Alon; Saks; Seymour
Conjecture If
is a simple graph which can be written as an union of
edge-disjoint complete bipartite graphs, then
.



Keywords: coloring; complete bipartite graph; eigenvalues; interlacing
Bounded colorings for planar graphs ★★
Author(s): Alon; Ding; Oporowski; Vertigan
Question Does there exists a fixed function
so that every planar graph of maximum degree
has a partition of its vertex set into at most three sets
so that for
, every component of the graph induced by
has size at most
?






Keywords: coloring; partition; planar graph