The On-Line Encyclopedia of Bongard Problems

Search: subworld:curves_drawing

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BP342

Exactly one axis of symmetry vs. either zero or more than one axis of symmetry.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP337 BP338 BP339 BP340 BP341 * BP343 BP344 BP345 BP346 BP347`
	KEYWORD	`traditional, finishedexamples`
	CONCEPT	`exists_one (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	WORLD	`shape_outline [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP390

Each graph vertex is uniquely defined by its connections (the graph does not admit nontrivial automorphisms) vs. the graph admits nontrivial automorphisms.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP385 BP386 BP387 BP388 BP389 * BP391 BP392 BP393 BP394 BP395`
	KEYWORD	`precise, allsorted, notso, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `self-reference (info \| search),` `topological_transformation (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP391

There exists an edge such that removing it yields two disconnected graphs (i.e., the minimum number of edges whose removal results in two disconnected graphs is 1) vs. the minimum number of edges whose removal results in two disconnected graphs is 2.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP386 BP387 BP388 BP389 BP390 * BP392 BP393 BP394 BP395 BP396`
	KEYWORD	`nice, precise, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `existence (info \| search),` `imagined_shape (info \| search),` `imagined_entity (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP557

Equal horizontal length vs. not

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	COMMENTS	`All examples in this Problem are pairs of straight line segments.` `This problem communicates the idea of projected distance, in this case from 2D to 1D (x-axis).`
	CROSSREFS	`Adjacent-numbered pages: BP552 BP553 BP554 BP555 BP556 * BP558 BP559 BP560 BP561 BP562`
	KEYWORD	`nice, precise, allsorted, stretch, perfect, unorderedpair, preciseworld`
	CONCEPT	`projection (info \| search)`
	WORLD	`two_segments [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

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`

BP562

There exists a closed trail that hits each vertex exactly once vs. not so.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`Left examples are called "Hamiltonian graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP557 BP558 BP559 BP560 BP561 * BP563 BP564 BP565 BP566 BP567`
	KEYWORD	`math, traditional`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP576

Vertices may be partitioned into two sets such that no two vertices in the same set are connected versus not so.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`Left examples are called "bipartite graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP571 BP572 BP573 BP574 BP575 * BP577 BP578 BP579 BP580 BP581`
	KEYWORD	`precise, allsorted, notso, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search)`
	WORLD	`graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP776

Four regions vs. less than four regions enclosed by straight lines

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	COMMENTS	`All examples in this Problem are a number of (possibly overlapping) straight lines.`
	CROSSREFS	`Adjacent-numbered pages: BP771 BP772 BP773 BP774 BP775 * BP777 BP778 BP779 BP780 BP781`
	WORLD	`segments_cross [smaller \| same \| bigger]`
	AUTHOR	`Finn Collins`

BP788

Graph contains a "loop" a.k.a. cycle (cyclic) versus graph is acyclic.

(edit; present; nest [left/right]; search; history)

	CROSSREFS	`Adjacent-numbered pages: BP783 BP784 BP785 BP786 BP787 * BP789 BP790 BP791 BP792 BP793`
	KEYWORD	`nice, precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `loop (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP809

Figures can be transformed into one another by smooth stretching (before and after there are the same crossroad-points; there is a curve connecting points before if and only if there is a curve connecting those points after) vs. not so.

(edit; present; nest [left/right]; search; history)

	COMMENTS	`Left examples are topologically homeomorphic figures.` `For some examples one can imagine pulling the shape "out of" the 2d square in 3d in order to transform it, and then laying it flat back in the 2d square. See BP810 for the version where this is not allowed.`
	CROSSREFS	`Adjacent-numbered pages: BP804 BP805 BP806 BP807 BP808 * BP810 BP811 BP812 BP813 BP814`
	KEYWORD	`nice, math, unorderedpair, traditional`
	CONCEPT	`topological_transformation (info \| search)`
	WORLD	`two_figures_made_of_curves [smaller \| same \| bigger] zoom in left (two_homeomorphic_figures_made_of_curves)`
	AUTHOR	`Aaron David Fairbanks`

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