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Hindman proved in 1979 that no matter how natural numbers are colored in r colors, for a fixed positive integer r, there is an infinite subset X of numbers and a color t such that for any finite non-empty subset X' of X, the color of the sum of eleme
Externí odkaz:
http://arxiv.org/abs/2109.10249
For each positive integer $n$, the Fibonacci-sum graph $G_n$ on vertices $1,2,\ldots,n$ is defined by two vertices forming an edge if and only if they sum to a Fibonacci number. It is known that each $G_n$ is bipartite, and all Hamiltonian paths in e
Externí odkaz:
http://arxiv.org/abs/1710.10303
It is shown that for $n\geq 141$, among all triangle-free graphs on $n$ vertices, the complete equibipartite graph is the unique triangle-free graph with the greatest number of cycles.
Externí odkaz:
http://arxiv.org/abs/1501.01088
Autor:
Füredi, Zoltan, Gunderson, David S.
Publikováno v:
Combinator. Probab. Comp. 24 (2014) 641-645
We describe the C_{2k+1}-free graphs on n vertices with maximum number of edges. The extremal graphs are unique except for n = 3k-1, 3k, 4k-2, or 4k-1. The value of ex(n,C_{2k+1}) can be read out from the works of Bondy, Woodall, and Bollobas, but he
Externí odkaz:
http://arxiv.org/abs/1310.6766
Publikováno v:
Discrete Mathematics 338 (2015) pp. 274-290
We conjecture that the balanced complete bipartite graph $K_{\lfloor n/2 \rfloor,\lceil n/2 \rceil}$ contains more cycles than any other $n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for
Externí odkaz:
http://arxiv.org/abs/1310.5172
Autor:
Gunderson, David W.
The thesis develops a FY 95 manday rate for a Shore Intermediate Maintenance Activity (SIMA) using Department of Defense Financial Management Regulations (DoD FMR) for Defense Business Operations Fund (DBOF) Operations in support of Regional Maintena
Externí odkaz:
http://hdl.handle.net/10945/32081
Publikováno v:
In Discrete Mathematics 6 February 2016 339(2):699-711
Publikováno v:
In Discrete Mathematics 6 February 2015 338(2):274-290
Autor:
Gunderson, David
This book, 768 pages long, contains material for use in Combinatorial Geometry (MATH 4300/7300). As a bonus, a fairly extensive review of elementary Euclidean geometry is given, which can be used in a variety of courses, including contest training. T
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_______217::e11afc4438d4b845d8f5ca060bd697ea
https://hdl.handle.net/1993/37002
https://hdl.handle.net/1993/37002