Bold Conjecture
المؤلف:
Sakuma, T.
المصدر:
"A Counterexample to the Bold Conjecture." J. Graph Th. 25
الجزء والصفحة:
...
21-4-2022
1906
Bold Conjecture
A pair of vertices 
of a graph 
is called an 
-critical pair if 
, where 
denotes the graph obtained by adding the edge 
to 
and 
is the clique number of 
. The 
-critical pairs are never edges in 
. A maximal stable set 
of 
is called a forced color class of 
if 
meets every 
-clique of 
, and 
-critical pairs within 
form a connected graph.
In 1993, G. Bacsó conjectured that if 
is a uniquely 
-colorable perfect graph, then 
has at least one forced color class. This conjecture is called the bold conjecture, and implies the strong perfect graph theorem. However, a counterexample of the conjecture was subsequently found by Sakuma (1997).
REFERENCES
Sakuma, T. "A Counterexample to the Bold Conjecture." J. Graph Th. 25, 165-168, 1997.
Sebő, A. "On Critical Edges in Minimal Perfect Graphs." J. Combin. Th. B 67, 62-85, 1996.
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