On hamiltonian line graphs of hypergraphs
Xiaofeng Gu, Hong‐Jian Lai, Sulin Song · Journal of Graph Theory · 2022
Abstract A graph is supereulerian if it has a spanning eulerian subgraph. Harary and Nash‐Williams in 1968 proved that the line graph of a graph is hamiltonian if and only if has a dominating eulerian subgraph, Jaeger in 1979 showed that every 4‐edge‐connected graph is supereulerian, and Catlin in 1988 proved that every graph with two edge‐disjoint spanning trees is a contractible configuration for supereulerianicity. Utilizing the notion of partition‐connectedness of hypergraphs introduced by Frank, Király, and Kriesell in 2003, we generalize the above‐mentioned results of Harary and Nash‐Williams, of Jaeger and of Catlin to hypergraphs by characterizing hypergraphs whose line graphs are hamiltonian, and showing that every 2‐partition‐connected hypergraph is a contractible configuration for supereulerianicity.