JCO
2007
13 years 11 months ago
2007
We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge ...
ENDM
2007
13 years 11 months ago
2007
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree ∆ ≥ 8 is at most 3
ENDM
2007
13 years 11 months ago
2007
The circular chromatic number of a graph is a well-studied refinement of the chromatic number. Circular-perfect graphs is a superclass of perfect graphs defined by means of this...
JCT
2006
13 years 11 months ago
2006
Let V be a vector space of dimension v over a field of order q. The q-Kneser graph has the kdimensional subspaces of V as its vertices, where two subspaces and are adjacent if and...
JSYML
2008
13 years 11 months ago
2008
We show that if add(null) = c, then the globally Baire and universally measurable chromatic numbers of the graph of any Borel function on a Polish space are equal and at most three...
JGT
2008
13 years 11 months ago
2008
: This article proves the following result: Let G and G be graphs of orders n and n , respectively. Let G be obtained from G by adding to each vertex a set of n degree 1 neighbors....
IPL
2008
13 years 11 months ago
2008
Colouring a graph with its chromatic number of colours is known to be NP-hard. Identifying an algorithm in which descisions are made locally with no information about the graph�...
EJC
2006
13 years 11 months ago
2006
The general symplectic graph Sp(2, q) is introduced. It is shown that Sp(2, q) is strongly regular. Its parameters are computed, its chromatic number and group of graph automorphis...
DM
2006
13 years 11 months ago
2006
For an integer r > 0, a conditional (k, r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent t...
COMBINATORICS
2006
13 years 11 months ago
2006
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....