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- Massachusetts Institute of TechnologyUS194 papers
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21 papers · 1 filter
Graphs missing a connected partition
Foster Tom
We prove that a graph with a cut vertex whose deletion produces at least five connected components must be missing a connected partition of some type. We prove that this also holds…
Enumerative and Structural Aspects Of Anagrams Without Fixed Letters
Kiril Bangachev
For the word denote by the number of its anag…
New Classes of Set-Sequential Trees
Louis Golowich, Chiheon Kim
A graph is called set-sequential if its vertices can be labeled with distinct nonzero vectors in such that when each edge is labeled with the sum of its…
A note on the Borwein conjecture
Jiyou Li
A conjecture of Borwein asserts that for any positive integers and , the coefficient of in the expansion of is non…
Linear bounds on matrix extremal functions using visibility hypergraphs
Jesse Geneson, Lilly Shen
The 0-1 matrix A contains a 0-1 matrix M if some submatrix of A can be transformed into M by changing some ones to zeroes. If A does not contain M, then A avoids M. Let ex(n,M) be…
Compatible Hamilton cycles in Dirac graphs
Michael Krivelevich, Choongbum Lee, Benny Sudakov
A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once. A celebrated theorem of Dirac from 1952 asserts that every graph on vertices with…