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BP560 There exists a closed trail that hits each edge exactly once vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Left examples are called "Eulerian graphs."


A connected graph is Eulerian if and only if each vertex is incident to an even number of edges.

CROSSREFS

Adjacent-numbered pages:
BP555 BP556 BP557 BP558 BP559  *  BP561 BP562 BP563 BP564 BP565

KEYWORD

precise, allsorted, math, traditional, preciseworld

CONCEPT graph (info | search),
distinguishing_crossing_curves (info | search),
all (info | search),
even_odd (info | search),
existence (info | search)

WORLD

connected_graph [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1100 There is a path between any two nodes vs. not so.
(edit; present; nest [left/right]; search; history)
REFERENCE

https://en.wikipedia.org/wiki/Graph_theory

https://en.wikipedia.org/wiki/Connectivity_(graph_theory)

CROSSREFS

Adjacent-numbered pages:
BP1095 BP1096 BP1097 BP1098 BP1099  *  BP1101 BP1102 BP1103 BP1104 BP1105

KEYWORD

precise, allsorted, world, preciseworld

CONCEPT graph (info | search),
distinguishing_crossing_curves (info | search),
connected_component (info | search)

WORLD

graph [smaller | same | bigger]
zoom in left (connected_graph) | zoom in right (disconnected_graph)

AUTHOR

Leo Crabbe

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