GroetzschGraph returns the smallest triangle-free graph with chromatic number 4. This is identical to MycielskiGraph[4].

HamiltonianPath[g] finds a Hamiltonian path in graph g if one exists. HamiltonianPath[g, All] gives all Hamiltonian paths of graph g.

HamiltonianQ[g] yields True if there exists a Hamiltonian cycle in graph g, or in other words, if there exists a cycle that visits each vertex exactly once.

Harary[k, n] constructs the minimal k-connected graph on n vertices.

HasseDiagram[g] constructs a Hasse diagram of the relation defined by directed acyclic graph g.

HeawoodGraph returns a smallest (6, 3)-cage, a 3-regular graph with girth 6.

HideCycles[c] canonically encodes the cycle structure c into a unique permutation.

HighlightedEdgeColors is an option to Highlight that determines which colors are used for the highlighted edges.

HighlightedEdgeStyle is an option to Highlight that determines how the highlighted edges are drawn.

HighlightedVertexColors is an option to Highlight that determines which colors are used for the highlighted vertices.