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

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Publication Date

8-20-2016

Document Type

Article

Department, Program, or Center

Computer Science (GCCIS)

Campus

RIT – Main Campus

Available for download on Saturday, July 13, 2019

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