DAM
2011
13 years 7 months ago
2011
A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic ...
COMGEO
2011
ACM
13 years 7 months ago
2011
ACM
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum ...
SIAMDM
2010
13 years 11 months ago
2010
K¨orner and Malvenuto asked whether one can find n n/2 linear orderings (i.e., permutations) of the first n natural numbers such that any pair of them places two consecutive int...
SIAMCOMP
2002
14 years 5 days ago
2002
A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. The domatic number problem is that of partitioning the vertices of a gra...
ENDM
2002
14 years 10 days ago
2002
Given a positive integer n and a family F of graphs, let R(n, F) denote the maximum number of colors in an edge-coloring of Kn such that no subgraph of Kn belonging to F has disti...
DM
2002
14 years 10 days ago
2002
We propose two new classes of non-adaptive pooling designs. The first one is guaranteed to be
DM
2002
14 years 10 days ago
2002
We investigate the minimum and maximum number of colors in edge-colorings of Kn,n such that every copy of Kp,p receives at least q and at most q colors. Along the way we improve t...
DM
2002
14 years 10 days ago
2002
For every nonnegative integer arc weight function
DM
2002
14 years 10 days ago
2002
Let G be a tree and let H be a collection of subgraphs of G, each having at most d connected components. Let (H) denote the maximum number of members of H no two of which share a ...
DCG
2002
14 years 10 days ago
2002
Let f(n) be the maximum number of unit distances determined by the vertices of a convex n-gon. Erdos and Moser conjectured that this function is linear. Supporting this conjecture...