Line perfect graphs

@article{Trotter1977LinePG,
  title={Line perfect graphs},
  author={L. Trotter},
  journal={Mathematical Programming},
  year={1977},
  volume={12},
  pages={255-259}
}
  • L. Trotter
  • Published 1977
  • Mathematics, Computer Science
  • Mathematical Programming
The concept of line perfection of a graph is defined so that a simple graph is line perfect if and only if its line graph is perfect in the usual sense. Line perfect graphs are characterized as those which contain no odd cycles of size larger than 3. 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 theorems. 
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References

SHOWING 1-10 OF 16 REFERENCES
The strong perfect-graph conjecture is true for K1, 3-free graphs
TLDR
Berge's strong perfect-graph conjecture is shown to be true for graphs which do not have K1, 3 as an induced subgraph and the line graphs thus belong to the class of graphs for which the conjecture is true. Expand
Normal hypergraphs and the perfect graph conjecture
A hypergraph is called normal if the chromatic index of any partial hypergraph H' of it coincides with the maximum valency in H'. It is proved that a hypergraph is normal iff the maximum number ofExpand
On the Perfect Graph Theorem
Publisher Summary This chapter provides an overview of perfect graph theorem. A version of the perfect graph theorem says, “Let A be a (0, l)-matrix such that the linear program yA w, y 0, min 1. yExpand
Paths, Trees, and Flowers
A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. AnExpand
Simple Constructions for Balanced Incomplete Block Designs with Block Size Three
TLDR
This paper provides a simpler proof for this case of a sequence of three-element subsets of S such that each two-element subset of S is contained in exactly λ terms of the sequence if and only if λ(v − 1) 2 and λv(v + 1) 6 are integers. Expand
A Characterization of Perfect Graphs
Throughout this note, graph means finite, undirected graph without loops and multiple edges.
Maximum matching and a polyhedron with 0,1-vertices
TLDR
The emphasis in this paper is on relating the matching problem to the theory of continuous linear programming, and the algorithm described does not involve any "blind-alley programming" -which, essentially, amounts to testing a great many combinations. Expand
Establishing the matching polytope
Abstract This paper gives an elementary, inductive proof-“graphical” in spirit-of a theorem of Edmonds' which specifies the convex hull of the matchings of an arbitrary, finite, undirected graph inExpand
Blocking and anti-blocking pairs of polyhedra
Some of the main notions and theorems about blocking pairs of polyhedra and antiblocking pairs of polyhedra are described. The two geometric duality theories conform in many respects, but there areExpand
Anti-blocking polyhedra
A theory parallel to that for blocking pairs of polyhedra is developed for anti-blocking pairs of polyhedra, and certain combinatorial results and problems are discussed in this framework. Expand
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