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A class of ?-perfect graphs
Finding Skew Partitions Efficiently
TLDR
This work presents a polynomial-time algorithm for testing whether a graph admits a skew partition, and solves the more general list skew partition problem, where the input contains, for each vertex, a list containing some of the labels of the four parts.
Clique Graph Recognition Is NP-Complete
TLDR
The clique graph recognition problem is NP-complete because there exists a graph H such that G=K(H) and there is no graph G such that H is a cliqueGraph.
Optimizing Bull-Free Perfect Graphs
TLDR
Here are polynomial-time combinatorial algorithms for the optimal weighted coloring and weighted clique problems in bull-free perfect graphs based on a structural analysis and decomposition of bull- free perfect graphs.
SPLITTING NUMBER is NP-complete
TLDR
The splitting number of a graph G is the smallest integer k 0, such that a planar graph can be obtained from G by k splitting operations, and it is proved that the splitting number decision problem is NP-complete.
Local Conditions for Edge-Coloring
In this note, we investigate three versions of the overfull property for graphs and their relation to the edge-coloring problem. Each of these properties implies that the graph cannot be edge-colored
An Improved Upper Bound on the Crossing Number of the Hypercube
TLDR
It is shown that the n-dimensional hypercube in the plane with 4 n-n-2+1+1 over 2 crossings improves the previous best estimation and coincides with the long conjectured upper bound of Erdos and Guy.
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