12 years 11 months ago
On the b-coloring of P4-tidy graphs
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 ...
Clara Inés Betancur Velasquez, Flavia Bonom...
12 years 11 months ago
A computational approach to Conway's thrackle conjecture
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 ...
Radoslav Fulek, János Pach
128views more  SIAMDM 2010»
13 years 2 months ago
Permutation Capacities of Families of Oriented Infinite Paths
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...
Graham Brightwell, Gérard D. Cohen, Emanuel...
139views more  SIAMCOMP 2002»
13 years 3 months ago
Approximating the Domatic Number
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...
Uriel Feige, Magnús M. Halldórsson, ...
107views more  ENDM 2002»
13 years 4 months ago
Edge-Colorings of Complete Graphs that Avoid Polychromatic Trees
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...
Tao Jiang, Douglas B. West
93views more  DM 2002»
13 years 4 months ago
New constructions of non-adaptive and error-tolerance pooling designs
We propose two new classes of non-adaptive pooling designs. The first one is guaranteed to be
Hung Q. Ngo, Ding-Zhu Du
81views more  DM 2002»
13 years 4 months ago
On restricted edge-colorings of bicliques
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...
Dhruv Mubayi, Douglas B. West
98views more  DM 2002»
13 years 4 months ago
On dijoins
For every nonnegative integer arc weight function
Gérard Cornuéjols, Bertrand Guenin
134views more  DM 2002»
13 years 4 months ago
Covering a hypergraph of subgraphs
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 ...
Noga Alon
76views more  DCG 2002»
13 years 4 months ago
The Unit Distance Problem for Centrally Symmetric Convex Polygons
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...
Bernardo M. Ábrego, Silvia Fernández...