600 research outputs found
A new proof of the graph removal lemma
Let H be a fixed graph with h vertices. The graph removal lemma states that
every graph on n vertices with o(n^h) copies of H can be made H-free by
removing o(n^2) edges. We give a new proof which avoids Szemer\'edi's
regularity lemma and gives a better bound. This approach also works to give
improved bounds for the directed and multicolored analogues of the graph
removal lemma. This answers questions of Alon and Gowers.Comment: 17 page
Cycles are strongly Ramsey-unsaturated
We call a graph H Ramsey-unsaturated if there is an edge in the complement of
H such that the Ramsey number r(H) of H does not change upon adding it to H.
This notion was introduced by Balister, Lehel and Schelp who also proved that
cycles (except for ) are Ramsey-unsaturated, and conjectured that,
moreover, one may add any chord without changing the Ramsey number of the cycle
, unless n is even and adding the chord creates an odd cycle.
We prove this conjecture for large cycles by showing a stronger statement: If
a graph H is obtained by adding a linear number of chords to a cycle ,
then , as long as the maximum degree of H is bounded, H is either
bipartite (for even n) or almost bipartite (for odd n), and n is large.
This motivates us to call cycles strongly Ramsey-unsaturated. Our proof uses
the regularity method
Partitioning 3-colored complete graphs into three monochromatic cycles
We show in this paper that in every 3-coloring of the edges of Kn all but o(n)
of its vertices can be partitioned into three monochromatic cycles. From this, using
our earlier results, actually it follows that we can partition all the vertices into at
most 17 monochromatic cycles, improving the best known bounds. If the colors of
the three monochromatic cycles must be different then one can cover ( 3
4 â o(1))n
vertices and this is close to best possible
Meritocracia y polĂtica interna en las organizaciones pĂșblicas: el caso de la Academia HĂșngara de las Ciencias
Tesis inĂ©dita de la Universidad Complutense de Madrid, Facultad de Ciencias EconĂłmicas y Empresariales, Departamento de OrganizaciĂłn de Empresas, leĂda el 15-12-2015Depto. de OrganizaciĂłn de EmpresasFac. de Ciencias EconĂłmicas y EmpresarialesTRUEunpu
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