# On line perfect graphs

@article{Werra1978OnLP,
title={On line perfect graphs},
author={D. Werra},
journal={Mathematical Programming},
year={1978},
volume={15},
pages={236-238}
}
• D. Werra
• Published 1978
• Mathematics, Computer Science
• Mathematical Programming
Line-perfect graphs have been defined by L.E. Trotter as graphs whose line-graphs are perfect. They are characterized by the property of having no elementary odd cycle of size larger than 3. L.E. Trotter showed constructively that the maximum cardinality of a set of mutually non-adjacent edges (matching) is equal to the minimum cardinality of a collection of sets of mutually adjacent edges which cover all edges.The purpose of this note is to give an algorithmic proof that the chromatic index of… Expand
29 Citations

#### Topics from this paper

Perfect k-line graphs and k-total graphs
• V. B. Le
• Mathematics, Computer Science
• J. Graph Theory
• 1993
The Perfect Graph Conjecture will be proved for 3-line graphs and 3-total graphs and perfect 3- line graphs are not contained in any of the known classes of perfect graphs. Expand
Partial characterizations of coordinated graphs: line graphs and complements of forests
• Mathematics, Computer Science
• Math. Methods Oper. Res.
• 2009
A partial result is presented, that is, coordinated graphs are characterized by minimal forbidden induced subgraphs when the graph is either a line graph, or the complement of a forest. Expand
Bicolored matchings in some classes of graphs
• Mathematics, Computer Science
• Electron. Notes Discret. Math.
• 2005
For regular bipartite graphs with n nodes on each side, sufficient conditions for the existence of a set R with |R|=n+1 such that perfect matchings with k red edges exist for all k,0?k?n. Expand
Classes of perfect graphs
• S. Hougardy
• Computer Science, Mathematics
• Discret. Math.
• 2006
This paper surveys 120 new classes of graphs, survey 120 of these classes, list their fundamental algorithmic properties and present all known relations between them. Expand
On 4-critical t-perfect graphs
This paper shows a new example of a 4-critical $t-perfect graph: the complement of the line graph of the 5-wheel$W_5$and proves that these two examples are in fact the only 4- critical graphs in the class of complements of line graphs. Expand The Strong Perfect Graph Theorem for a Class of Partitionable Graphs • Mathematics • 1984 A simple adjacency criterion is presented which, when satisfied, implies that a minimal imperfect graph is an odd hole or an odd antihole. For certain classes of graphs, including K 1,3 -free graphs,Expand Some conjectures on perfect graphs • V. B. Le • Computer Science, Mathematics • Discuss. Math. Graph Theory • 2000 The Perfect Graph Theorem used to be the so-called weak perfect graph conjecture posed by C. Berge around 1960s, but now it is the stronger conjecture, which is still open, is as follows. Expand Perfectness is an Elusive Graph Property • Mathematics, Computer Science • SIAM J. Comput. • 2004 It is proved that a nonmonotone but hereditary graph property is elusive: perfectness. Expand Minimum Weighted Clique Cover on Strip-Composed Perfect Graphs • Mathematics, Computer Science • WG • 2012 This paper shows that a mwcc of a perfect strip-composed graph, with the basic graphs belonging to a class${\cal G}\$, can be found in polynomial time, and designs a new, more efficient, combinatorial algorithm for the mwCC problem on strip- Composed claw-free perfect graphs. Expand
Bicolored Matchings in Some Classes of Graphs
• Mathematics, Computer Science
• Graphs Comb.
• 2007
A linear time algorithm is designed to determine a minimum set R of red edges such that there exist maximum matchings with k red edges for the largest possible number of values of k. Expand

#### References

SHOWING 1-2 OF 2 REFERENCES
Line perfect graphs
• L. Trotter
• Mathematics, Computer Science
• Math. Program.
• 1977
Two well-know theorems of König for bipartite graphs are shown to hold also for line perfect graphs; this extension provides a reinterpretation of the content of these theorem. Expand