On diameters and radii of bridged graphs
Discrete Mathematics
Structural properties and decomposition of linear balanced matrices
Mathematical Programming: Series A and B
Testing balancedness and perfection of linear matrices
Mathematical Programming: Series A and B
Decomposition of balanced matrices
Journal of Combinatorial Theory Series B
A class of &bgr;-perfect graphs
Discrete Mathematics
Balanced 0, ±1 matrices I. decomposition
Journal of Combinatorial Theory Series B
Decomposition of odd-hole-free graphs by double star cutsets and 2-joins
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
Combinatorica
A polynomial recognition algorithm for balanced matrices
Journal of Combinatorial Theory Series B
Algorithms for Perfectly Contractile Graphs
SIAM Journal on Discrete Mathematics
Even and odd holes in cap-free graphs
Journal of Graph Theory
Even-hole-free graphs part I: Decomposition theorem
Journal of Graph Theory
Even-hole-free graphs part II: Recognition algorithm
Journal of Graph Theory
Journal of Graph Theory
SIAM Journal on Discrete Mathematics
Claw-free graphs. IV. Decomposition theorem
Journal of Combinatorial Theory Series B
Bisimplicial vertices in even-hole-free graphs
Journal of Combinatorial Theory Series B
Even-hole-free graphs that do not contain diamonds: A structure theorem and its consequences
Journal of Combinatorial Theory Series B
A structure theorem for graphs with no cycle with a unique chord and its consequences
Journal of Graph Theory
Combinatorica
Combinatorial optimization with 2-joins
Journal of Combinatorial Theory Series B
The structure of bull-free graphs II and III-A summary
Journal of Combinatorial Theory Series B
A faster algorithm to recognize even-hole-free graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Journal of Discrete Algorithms
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In this paper we consider the class of simple graphs defined by excluding, as induced subgraphs, even holes (i.e. chordless cycles of even length). These graphs are known as even-hole-free graphs. We prove a decomposition theorem for even-hole-free graphs, that uses star cutsets and 2-joins. This is a significant strengthening of the only other previously known decomposition of even-hole-free graphs, by Conforti, Cornuejols, Kapoor and Vuskovic, that uses 2-joins and star, double star and triple star cutsets. It is also analogous to the decomposition of Berge (i.e. perfect) graphs with skew cutsets, 2-joins and their complements, by Chudnovsky, Robertson, Seymour and Thomas. The similarity between even-hole-free graphs and Berge graphs is higher than the similarity between even-hole-free graphs and simply odd-hole-free graphs, since excluding a 4-hole, automatically excludes all antiholes of length at least 6. In a graph that does not contain a 4-hole, a skew cutset reduces to a star cutset, and a 2-join in the complement implies a star cutset, so in a way it was expected that even-hole-free graphs can be decomposed with just the star cutsets and 2-joins. A consequence of this decomposition theorem is a recognition algorithm for even-hole-free graphs that is significantly faster than the previously known ones.