Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
419472 | Discrete Applied Mathematics | 2011 | 6 Pages |
Abstract
In 1995, Plummer (1992) [6] published a paper in which he gave a characterization of 4-regular, 4-connected, claw-free graphs. Based on that work, Hartnell and Plummer (1996) [5] published a paper on 4-connected, claw-free, well-covered graphs a year later. However, in his 1995 paper, Plummer inadvertently omitted some of the graphs with odd order. In this paper, we will complete Plummer’s characterization of all 4-connected, 4-regular, claw-free graphs, and then show the implications this has on the well-covered graphs he and Hartnell determined. In addition, we will characterize 4-connected, 4-regular, claw-free, well-dominated graphs.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Trevor J. Gionet Jr., Erika L.C. King, Yixiao Sha,