TY - JOUR
T1 - Long paths in heterogeneous random subgraphs of graphs with large minimum degree
AU - Shang, Yilun
PY - 2023/4/20
Y1 - 2023/4/20
N2 - For a graph Gk on n vertices with a minimum degree of at least k → ∞ as n → ∞, let G(n, p) be a random subgraph of Gk taken by retaining each edge (i, j) independently with probability pi j and p = {pi j}(i, j)∈Gk . We show that under certain conditions on the edge probabilities, the resulting random graph has a long path that covers almost all or all vertices with probability tending to 1 as n → ∞.
AB - For a graph Gk on n vertices with a minimum degree of at least k → ∞ as n → ∞, let G(n, p) be a random subgraph of Gk taken by retaining each edge (i, j) independently with probability pi j and p = {pi j}(i, j)∈Gk . We show that under certain conditions on the edge probabilities, the resulting random graph has a long path that covers almost all or all vertices with probability tending to 1 as n → ∞.
KW - Random graphs
KW - Path
KW - Subgraph
KW - Hamiltonian path
U2 - 10.1016/j.ipl.2023.106401
DO - 10.1016/j.ipl.2023.106401
M3 - Article
JO - Information Processing Letters
JF - Information Processing Letters
SN - 0020-0190
M1 - 106401
ER -