DisCoMath Seminar: Well, well, well..."well"ness in graph theory, especially well-forcedness
DisCoMath Seminar
Well, well, well… “well”ness in graph theory, especially well-forcedness
Dr. Bonnie Jacob
Rochester Institute of Technology
Abstract:
Many graph problems focus on finding the minimum value of a particular kind of vertex set on a graph. For example, finding minimum vertex covers or minimum dominating sets are non-trivial problems. For a few of these parameters, researchers have considered what graphs have the interesting property that every minimal 𝑋-set (where 𝑋 is your favorite minimizable graph parameter) is also a minimum 𝑋-set, and call such graphs well 𝑋ed. We start this talk by briefly looking at some examples of "well"ness among different parameters before delving into our research that applied this well idea to zero forcing. In our work, we introduced the concept of well-forced graphs, that is, graphs in which every minimal zero forcing set is a minimum zero forcing set. We were able to characterize well-forced trees, and along the way discovered some interesting properties of vertices that appear in no minimal zero forcing sets. We describe our results here and some open questions.
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Intended Audience:
All are welcome.
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