Abstract
We study properties of the sets of minimal forbidden minors for the families of graphs having a vertex cover of size at most k. We denote this set by O ( k-V ERTEX C OVER) and call it the set of obstructions. Our main result is to give a tight vertex bound of O ( k-V ERTEX C OVER), and then confirm a conjecture made by Liu Xiong that there is a unique connected obstruction with maximum number of vertices for k-V ERTEX C OVER and this graph is C 2 k + 1 . We also find two iterative methods to generate graphs in O ( ( k + 1 ) -V ERTEX C OVER) from any graph in O ( k-V ERTEX C OVER).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
