On graphs whose square have strong Hamiltonian properties

DOI10.1016/j.disc.2009.02.026zbMath1210.05121OpenAlexW2016126876MaRDI QIDQ1043996

J. Blot

Publication date: 10 December 2009

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2009.02.026

zbMATH Keywords

square of graphHamilton-connected graphpanconnected graph

Mathematics Subject Classification ID

Connectivity (05C40) Eulerian and Hamiltonian graphs (05C45) Graph operations (line graphs, products, etc.) (05C76)

Related Items (9)

Connected even factors in the square of essentially 2-edge-connected graph ⋮ A short proof of the versatile version of Fleischner's theorem ⋮ The most general structure of graphs with Hamiltonian or Hamiltonian connected square ⋮ Graphs with cyclomatic number three having panconnected square ⋮ Single-source three-disjoint path covers in cubes of connected graphs ⋮ Disjoint path covers in cubes of connected graphs ⋮ Graphs with cyclomatic number two having panconnected square ⋮ A linear-time algorithm for finding a paired 2-disjoint path cover in the cube of a connected graph ⋮ Graphs with cyclomatic number three having panconnected square, II

Cites Work

• The square of a block is vertex pancyclic
• In the square of graphs, Hamiltonicity and pancyclicity, Hamiltonian connectedness and panconnectedness are equivalent concepts
• On graphs with Hamiltonian squares
• The square of a block is Hamiltonian connected
• The square of a block is strongly path connected
• The square of every two-connected graph is Hamiltonian
• Trees with Hamiltonian square

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