Name
Abstract | ||
|---|---|---|
The famous Konig-Egervary theorem is equivalent to the statement that the matching number equals the vertex cover number for every induced subgraph of some graph if and only if that graph is bipartite. Inspired by this result, we consider the set G(k) of all graphs such that, for every induced subgraph, the maximum number of disjoint paths of order k equals the minimum order of a set of vertices intersecting all paths of order k. For k is an element of {3, 4}, we give complete structural descriptions of the graphs in G(k). Further-more, for odd k, we give a complete structural description of the graphs in G(k) that contain no cycle of order less than k. For these graph classes, our results yield efficient recognition algorithms as well as efficient algorithms that determine maximum sets of disjoint paths of order k and minimum sets of vertices intersecting all paths of order k. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1002/jgt.22421 | JOURNAL OF GRAPH THEORY |
Keywords | DocType | Volume |
k-path vertex cover,Konig-Egervary theorem,matching,vertex cover,bipartite graph | Journal | 91.0 |
Issue | ISSN | Citations |
1.0 | 0364-9024 | 0 |
PageRank | References | Authors |
0.34 | 7 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stéphane Bessy | 1 | 117 | 19.68 |
| Pascal Ochem | 2 | 258 | 36.91 |
| Dieter Rautenbach | 3 | 946 | 138.87 |