2020/04/01 by Carl Bürger, Bürger, Carl, Jan Kurkofka +1
Computer Science · #05C05 (Secondary) #05C40 #05C63 (Primary) #05C75 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2004.00593
openalex publication_date 2020/04/01 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In a series of four papers we determine structures whose existence is dual,\nin the sense of complementary, to the existence of stars or combs. Here, in the\nsecond paper of the series, we present duality theorems for combinations of\nstars and combs: dominating stars and dominated combs. As dominating stars\nexist if and only if dominated combs do, the structures complementary to them\ncoincide. Like for arbitrary stars and combs, our duality theorems for\ndominated combs (and dominating stars) are phrased in terms of normal trees or\ntree-decompositions.\n The complementary structures we provide for dominated combs unify those for\nstars and combs and allow us to derive our duality theorems for stars and combs\nfrom those for dominated combs. This is surprising given that our complementary\nstructures for stars and combs are quite different: those for stars are locally\nfinite whereas those for combs are rayless.\n