- In the
mathematical field of
graph theory, the
Grötzsch graph is a triangle-free
graph with 11 vertices, 20 edges,
chromatic number 4, and
crossing number...
- In the
mathematical field of
graph theory,
Grötzsch's theorem is the
statement that
every triangle-free
planar graph can be
colored with only
three colors...
-
Grötzsch or
Groetzsch may
refer to:
Herbert Grötzsch,
German mathematician Grötzsch,
German name for Grodziszcze, Żary County, a
village in
Poland Grötzsch...
-
Camillo Herbert Grötzsch (21 May 1902 – 15 May 1993) was a
German mathematician. He was born in Döbeln and died in Halle.
Grötzsch worked in
graph theory...
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chromatic number than H, then G and H are incomparable. For example, the
Grötzsch graph is 4-chromatic and triangle-free (it has
girth 4 and odd
girth 5)...
-
bipartite graph (that is,
every 2-colorable graph) is triangle-free, and
Grötzsch's theorem states that
every triangle-free
planar graph may be 3-colored...
- with two
vertices connected by an edge, the
cycle graph M3 = C5, and the
Grötzsch graph M4 with 11
vertices and 20 edges. In general, the
graph Mi is triangle-free...
- instance, the
Grötzsch graph is triangle-free and has
chromatic number 4, and
repeating the
Mycielskian construction used to form the
Grötzsch graph produces...
-
three independent color classes. It
contains as an
induced subgraph the
Grötzsch graph, the
smallest triangle-free four-chromatic graph, and
every four-chromatic...
-
cliques have a high
chromatic number, but the
opposite is not true. The
Grötzsch graph is an
example of a 4-chromatic
graph without a triangle, and the...
