![](/files/happy5.png)
Erdos, Paul
Monochromatic reachability in edge-colored tournaments ★★★
Author(s): Erdos
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ f(n) $](/files/tex/9579fe06c51fc31a993cd148e8bbc3cb07df464e.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ S $](/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png)
![$ f(n) $](/files/tex/9579fe06c51fc31a993cd148e8bbc3cb07df464e.png)
![$ S $](/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png)
Keywords: digraph; edge-coloring; tournament
Covering systems with big moduli ★★
![$ N $](/files/tex/e178f13e28934a284e7c8f31e0187aee6ebdf650.png)
![$ N $](/files/tex/e178f13e28934a284e7c8f31e0187aee6ebdf650.png)
Keywords: covering system
Odd incongruent covering systems ★★★
Keywords: covering system
Sets with distinct subset sums ★★★
Author(s): Erdos
Say that a set has distinct subset sums if distinct subsets of
have distinct sums.
![$ c $](/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png)
![$ |S| \le \log_2(n) + c $](/files/tex/493a86991ee82d34f35bf457f417ec42892b4c5f.png)
![$ S \subseteq \{1,2,\ldots,n\} $](/files/tex/c6a976583643131f2542c200da7e75610cb3772d.png)
Keywords: subset sum
The Erdos-Turan conjecture on additive bases ★★★★
Let . The representation function
for
is given by the rule
. We call
an additive basis if
is never
.
![$ B $](/files/tex/4369e4eb2b0938fb27436a8c4f4a062f83d4d49e.png)
![$ r_B $](/files/tex/9503779c20e2cdbf39f574df5eb6379cb82922d7.png)
Keywords: additive basis; representation function
Diagonal Ramsey numbers ★★★★
Author(s): Erdos
Let denote the
diagonal Ramsey number.
![$ \lim_{k \rightarrow \infty} R(k,k) ^{\frac{1}{k}} $](/files/tex/239db4dc95ea810751ae620dbaa3da745636e4cc.png)
Keywords: Ramsey number
Unions of triangle free graphs ★★★
![$ K_4 $](/files/tex/03778d11eadbb74fc862e7762ec7ce773f0b9413.png)
![$ \aleph_0 $](/files/tex/ae61eb32cc3c2cd0fc395f5f137af2ecebcc6f92.png)
Keywords: forbidden subgraph; infinite graph; triangle free
The Crossing Number of the Hypercube ★★
The crossing number of
is the minimum number of crossings in all drawings of
in the plane.
The -dimensional (hyper)cube
is the graph whose vertices are all binary sequences of length
, and two of the sequences are adjacent in
if they differ in precisely one coordinate.
![$ \displaystyle \lim \frac{cr(Q_d)}{4^d} = \frac{5}{32} $](/files/tex/8a347f2f5bc9527051396b3f7efcdc793f5c87f0.png)
Keywords: crossing number; hypercube
The Erdös-Hajnal Conjecture ★★★
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
![$ \delta(H) $](/files/tex/f3109c2657867bfbf5df1f9d878be062ffaa82d0.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
![$ |V(G)|^{\delta(H)} $](/files/tex/e12fe74b562523df4457275a178e2078c43c7715.png)
Keywords: induced subgraph
![Syndicate content Syndicate content](/misc/feed.png)