Seminarium Kombinatoryka, Teoria Grafów i Zbiorów Uporządkowanych
Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska
Kalendarz Środy, 10:15-11:45
Pinezka Gmach MiNI PW, Sala 431, ul. Koszykowa 75, Warszawa
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Najbliższy referat
27.05.2026 Marta Piecyk CISPA
List coloring ordered graphs with forbidden induced subgraphs
\(\quad\)In the List k-Coloring problem we are given a graph G whose every vertex is equipped with a list, which is a subset of {1,...,k} . We need to decide if G admits a proper coloring, where every vertex receives a color from its list. The complexity of the problem in classes defined by forbidding induced subgraphs is a widely studied topic in algorithmic graph theory. Recently, Hajebi, Li, and Spirkl [SIAM J. Discr. Math. 38 (2024)] initiated the study of List 3 -Coloring in ordered graphs, i.e., graphs with fixed linear ordering of vertices. Forbidding ordered induced subgraphs allows us to investigate the boundary of tractability more closely. We continue this direction of research, focusing mostly on the case of List 4-Coloring. We present several algorithmic and hardness results, which altogether provide an almost complete dichotomy for classes defined by forbidding one fixed ordered graph: our investigations leave one minimal open case. This is joint work with Paweł Rzążewski.
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