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 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 graphs 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 exactly ...

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 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 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 it ...

. 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, it ...

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..

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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