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JCO

2007

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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

10 years 1 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, . . ....