David P. Sumner is an American mathematician known for his research in
graph theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...
. He formulated
Sumner's conjecture that
tournaments
A tournament is a competition involving at least three competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses:
# One or more competitions held at a single venue and concentr ...
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 graph
In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph.
A claw is another name for the complete bipartite graph ''K''1,3 (that is, a star graph comprising three edges, three leaves, ...
s with an even number of vertices have
perfect matching
In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph , a perfect matching in is a subset of edge set , such that every vertex in the vertex set is adjacent to exactl ...
s. 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 sta ...
independently formulated the
Gyárfás–Sumner conjecture according to which, for every
tree
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...
''T'', the ''T''-free graphs are
χ-bounded
In graph theory, a \chi-bounded family \mathcal of graphs is one for which there is some function c such that, for every integer t the graphs in \mathcal with t=\omega(G) (clique number) can be colored with at most c(t) colors. This concept and its ...
.
Sumner earned his doctorate from the
University of Massachusetts Amherst
The University of Massachusetts Amherst (UMass Amherst, UMass) is a public research university in Amherst, Massachusetts and the sole public land-grant university in Commonwealth of Massachusetts. Founded in 1863 as an agricultural college, ...
in 1970, under the supervision of
David J. Foulis. 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