کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
420608 | 683961 | 2008 | 13 صفحه PDF | دانلود رایگان |

Circular-perfect graphs form a natural superclass of perfect graphs: on the one hand due to their definition by means of a more general coloring concept, on the other hand as an important class of χχ-bound graphs with the smallest non-trivial χχ-binding function χ(G)⩽ω(G)+1χ(G)⩽ω(G)+1.The Strong Perfect Graph Conjecture, recently settled by Chudnovsky et al. [The strong perfect graph theorem, Ann. of Math. 164 (2006) 51–229], provides a characterization of perfect graphs by means of forbidden subgraphs. It is, therefore, natural to ask for an analogous conjecture for circular-perfect graphs, that is for a characterization of all minimal circular-imperfect graphs.At present, not many minimal circular-imperfect graphs are known. This paper studies the circular-(im)perfection of some families of graphs: normalized circular cliques, partitionable graphs, planar graphs, and complete joins. We thereby exhibit classes of minimal circular-imperfect graphs, namely, certain partitionable webs, a subclass of planar graphs, and odd wheels and odd antiwheels. As those classes appear to be very different from a structural point of view, we infer that formulating an appropriate conjecture for circular-perfect graphs, as analogue to the Strong Perfect Graph Theorem, seems to be difficult.
Journal: Discrete Applied Mathematics - Volume 156, Issue 7, 1 April 2008, Pages 998–1010