Abstract
We study a new problem for cubic graphs: bipartization of a cubic graph Q by deleting sufficiently large independent set I. It can be expressed as follows: Given a connected n-vertex tripartite cubic graph Q = (V, E) with independence number α(Q), does Q contain an independent set I of size k such that Q − I is bipartite? We are interested for which value of k the answer to this question is affirmative. We prove constructively that if α(Q) ≥ 4n/10, then the answer is positive for each k fulfilling ⌊(n − α(Q))/2⌋ ≤ k ≤ α(Q). It remains an open question if a similar construction is possible for cubic graphs with α(Q) < 4n/10. Next, we show that this problem with α(Q) ≥ 4n/10 and k fulfilling inequalities ⌊n/3⌋ ≤ k ≤ α(Q) can be related to semi-equitable graph 3-coloring, where one color class is of size k, and the subgraph induced by the remaining vertices is equitably 2-colored. This means that Q has a coloring of type (k, ⌈(n − k)/2⌉, ⌊(n − k)/2⌋).
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Date
8-20-2016
Document Type
Article
Department, Program, or Center
Computer Science (GCCIS)
Recommended Citation
Hanna Furmańczyk, Marek Kubale, Stanisław Radziszowski, On bipartization of cubic graphs by removal of an independent set, Discrete Applied Mathematics, Volume 209, 2016, Pages 115-121, ISSN 0166-218X, http://dx.doi.org/10.1016/j.dam.2015.10.036.
Campus
RIT – Main Campus
