Let H and G be two graphs on fixed number of vertices. An edge coloring of a complete graph is called (H, G)-good if there is no monochromatic copy of G and no rainbow (totally multicolored) copy of H in this coloring. As shown by Jamison and West, an (H, G)-good coloring of an arbitrarily large complete graph exists unless either G is a star or H is a… (More)
This note contains a simplified proof of Anti-Ramsey theorem for cycles by Montellano-Ballesteros and Neumann-Lara , which was originally conjectured by Erd˝ os, Simonovits and Sós .
The chromatic number of a subset of the real plane is the smallest number of colors assigned to the elements of that set such that no two points at distance 1 receive the same color. It is known that the chromatic number of the plane is between 4 and 7. In this note, we determine the bounds on the chromatic number for several classes of subsets of the plane… (More)
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t For two graphs, G and H, an edge coloring of a complete graph is (G,… (More)