Coloring a graph optimally with two colors

AbstractLet G be a graph with point set V. A (2-)coloring of G is a map of V to {red, white}. An error occurs whenever the two endpoints of a line have the same color. An optimal coloring of G is a coloring of G for which the number of errors is minimum. The minimum number of errors is denoted by γ(G), we derive upper and lower bounds for γ(G) and prove that if G is a graph with n points and m lines, then max{0, m−⌊14n2⌋}⩽γ(G)⩽⌊12m−14(h(m)−1)⌋, where h(m)=min{n¦m⩽(n2)}. The lower bound is sharp, and for infinitely many values of m the upper bound is attained for all sufficiently large n

Rainbow Generalizations of Ramsey Theory - A Dynamic Survey

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs

Rainbow Generalizations of Ramsey Theory - A Dynamic Survey

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs