(SI) V okviru bilateralnega projekta se želimo posvetiti zgoraj naštetim problemom s sledeče nove perspektive: študij problemov v kontekstu dobro strukturiranih hereditarnih grafovskih razredov (npr. kografov, tetivnih grafov, razdaljno hereditarnih grafov ipd.); študij koncepta F-WORM barvanja glede na inducirane podgrafe. Upoštevaje znanja slovenske projektne skupine bomo preučili tudi možne povezave med F-WORM barvanji in dominacijo v grafih. Skupno raziskovalno področje obeh skupin predstavljajo grafi in hipergrafi. Menimo, da bi se na tem projektu znanje slovenske skupine, predvsem o strukturi grafovskih razredov, odlično dopolnjevalo z znanjem ameriške skupine s področja barvanj grafov in hipergrafov.
(EN) In the framework of the bilateral project, we want to address the above problems from the following new perspectives: study the problems in the context of well-structured hereditary graph classes (e.g., co graphs, chordal graphs, distance hereditary graphs, etc.); study the concept of F-WORM colouring with respect to induced subgraphs. Taking into account the knowledge of the Slovenian project team, we will also study possible connections between F-WORM colourings and dominance in graphs. Graphs and hypergraphs are common research areas for both groups. We believe that in this project the knowledge of the Slovenian group, in particular on the structure of graph classes, would be an excellent complement to the knowledge of the American group in the field of graph colourings and hypergraphs.