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| Content Provider | Society for Industrial and Applied Mathematics (SIAM) |
|---|---|
| Author | Metelsky, Yury Tyshkevich, Regina |
| Copyright Year | 2003 |
| Abstract | A natural generalization of the notion of domino introduced and investigated in [T. Kloks, D. Kratsch, and H. Mller, Dominoes, Lecture Notes in Comput. Sci. 903, Springer-Verlag, Berlin, 1995, pp. 106--120] is considered. A graph is called an r-mino if each of its vertices belongs to at most r maximal cliques. The class of r-minoes is denoted ${\cal M}_r.$ Thus ${\cal M}_2$ is the class of dominoes. It is shown that ${\cal M}_r$ coincides with the class of line graphs of Helly hypergraphs with rank at most r. For an arbitrary r, the existence of a finite list of forbidden induced subgraphs characterizing ${\cal M}_r$ is proved. An explicit finite characterization is given for ${\cal M}_3$. An r-mino is called linear if each of its edges belongs to exactly one maximal clique. We prove that the GRAPH 3-COLORABILITY problem remains NP-complete when restricted to linear dominoes with vertex degrees at most 4. |
| Starting Page | 438 |
| Ending Page | 448 |
| Page Count | 11 |
| File Format | |
| ISSN | 08954801 |
| DOI | 10.1137/S089548019936521X |
| e-ISSN | 10957146 |
| Journal | SIAM Journal on Discrete Mathematics (SJDMEC) |
| Issue Number | 3 |
| Volume Number | 16 |
| Language | English |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher Date | 2006-08-01 |
| Access Restriction | Subscribed |
| Subject Keyword | r-covering induced subgraph Structural characterization of families of graphs Helly hypergraph r-mino graph finite characterization hypergraph clique Factorization, matching, partitioning, covering and packing rank of hypergraph line graph of hypergraph Hypergraphs Graph representations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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