Flexible list colorings: Maximizing the number of requests satisfied
Hemanshu Kaul, Rogers Mathew, Jeffrey A. Mudrock, and Michael J., Pelsmajer

TL;DR
This paper advances the understanding of flexible list coloring in graphs, establishing new bounds on the fraction of requests that can be satisfied and introducing the concept of list flexibility number, with implications for graph coloring theory.
Contribution
It extends flexible list coloring results to bipartite $d$-degenerate graphs, improves bounds on flexibility, and introduces the list flexibility number linking various graph parameters.
Findings
Extended results to bipartite $d$-degenerate graphs.
Proved $d$-degenerate graphs are $(d+2, 1/2^{d+1})$-flexible.
Introduced the list flexibility number and explored its relationships with other graph invariants.
Abstract
Flexible list coloring was introduced by Dvo\v{r}\'{a}k, Norin, and Postle in 2019. Suppose , is a graph, is a list assignment for , and is a function with non-empty domain such that for each ( is called a request of ). The triple is -satisfiable if there exists a proper -coloring of such that for at least vertices in . We say is -flexible if is -satisfiable whenever is a -assignment for and is a request of . It was shown by Dvo\v{r}\'{a}k et al. that if is prime, is a -degenerate graph, and is a request for with domain of size , then is -satisfiable whenever is a -assignment. In this paper, we extend this result to all for…
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Taxonomy
TopicsScheduling and Timetabling Solutions · Supply Chain and Inventory Management
