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Progress on the Hall-number-two problem
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Progress on the Hall-number-two problem

Eslahchi, C

Progress on the Hall-number-two problem

Eslahchi, C ; Sharif University of Technology | 2000

1389 Viewed
  1. Type of Document: Article
  2. Publisher: 2000
  3. Abstract:
  4. The graphs with Hall number at most 2 form a class of graphs within which the chromatic number equals the choice (list-chromatic) number. This class has a forbidden-induced-subgraph characterization which has not yet been found, although a fairly imposing collection of minimal forbidden induced subgraphs has been assembled. In this paper we add to the collection, most notably adding (i) K5 with an ear of length 2 attached; (ii) K4 with an ear of any length> 2 attached; (iii) any cycle together with two triangles based on incident edges on the cycle; (iv) any odd cycle together with two triangles based on non-incident edges of the cycle; and (v) any even cycle together with three triangles based on non-incident edges of the cycle
  5. Keywords:
  7. Source: Australasian Journal of Combinatorics ; Volume 21 , 2000 , Pages 211-236 ; 10344942 (ISSN)
  8. URL: https://ajc.maths.uq.edu.au/pdf/21/ocr-ajc-v21-p211.pdf