Dates: 29 April-3 May 2019
Structural graph theory studies characterizations and decompositions of particular graph classes, and uses these results to prove theoretical properties from such graph classes as well as to derive various algorithmic consequences. Several major graph coloring problems were resolved using tools of structural graph theory, including the special case of Hadwiger's conjecture for graphs avoiding K_6 as a minor (1993) and the Strong Perfect Graph Conjecture (2006). Since then, these tools were established as fundamental to many new developments in the theory of graph colorings. Conversely, graph coloring results are often used to motivate or obtain interesting structural decompositions; as an example, substantial progress in the study of nowhere-dense classes was made using their low tree-depth colorings.
The proposed workshop will build upon this fruitful interplay between the fields of graph coloring and structural graph theory. It will bring together leading experts in the fields, giving them an opportunity to learn about the state of the art in the respective areas, to disseminate newly developed methods, and to work jointly towards resolving the current challenges.
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