David P. Sumner is an American mathematician known for his research in
graph theory. He formulated
Sumner's conjecture
Sumner's conjecture (also called Sumner's universal tournament conjecture) states that every orientation of every n-vertex tree is a subgraph of every (2n-2)-vertex tournament.
David Sumner, a graph theorist at the University of South Carolina ...
that
tournaments are
universal graph In mathematics, a universal graph is an infinite graph that contains ''every'' finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type was first constructed by Richard Rado and is now called the Rado graph or ...
s for
polytree
In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree; . or singly connected network.) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, if we replace its ...
s in 1971, and showed in 1974 that all
claw-free graphs with an even number of vertices have
perfect matchings. He and
András Gyárfás
András Gyárfás (born 1945) is a Hungarian mathematician who specializes in the study of graph theory. He is famous for two conjectures:
* Together with Paul Erdős he conjectured what is now called the Erdős–Gyárfás conjecture which s ...
independently formulated the
Gyárfás–Sumner conjecture
In graph theory, the Gyárfás–Sumner conjecture asks whether, for every tree T and complete graph K, the graphs with neither T nor K as induced subgraphs can be properly colored using only a constant number of colors. Equivalently, it asks whet ...
according to which, for every
tree ''T'', the ''T''-free graphs are
χ-bounded.
Sumner earned his doctorate from the
University of Massachusetts Amherst in 1970, under the supervision of
David J. Foulis
David James Foulis (July 26, 1930- April 3, 2018) was an American mathematician known for his research on the algebraic foundations of quantum mechanics.
He spent much of his career at the University of Massachusetts Amherst,. retiring in 1997 b ...
. He is a distinguished professor emeritus at the
University of South Carolina.
[.]
References
External links
Home page
Year of birth missing (living people)
Living people
20th-century American mathematicians
University of Massachusetts Amherst alumni
University of South Carolina faculty
Graph theorists
Place of birth missing (living people)
{{US-mathematician-stub