DAM

2011

12 years 11 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

12 years 11 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 2 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

13 years 3 months 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

13 years 4 months 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

13 years 4 months ago
2002

We propose two new classes of non-adaptive pooling designs. The first one is guaranteed to be

DM

2002

13 years 4 months 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

13 years 4 months ago
2002

For every nonnegative integer arc weight function

DM

2002

13 years 4 months 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

13 years 4 months 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...