Some properties of grid homology for MOY graphs

Grid homology, a combinatorial version of link Floer homology introduced by Manolescu, Ozsváth, Szabó, Thurston [On combinatorial link Floer homology, Geom. Topol. 11 (2007) 2339–2412, MR 2372850], has been extended to transverse spatial graphs by Harvey and O’Donnol [Heegaard Floer homology of spatial graphs, Algebr. Geom. Topol. 17(3) (2017) 1445–1525, MR 3677933]. In this paper, we define grid homology for MOY graphs, a specific class of transverse spatial graphs, and show properties such as the oriented skein relation, the effect of contracting an edge, and the effect of uniting parallel edges with the same orientation.