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#open-problem-garden

Problems and findings carrying the open-problem-garden tag.

Problems (13)

Newest Activity Importance Tractability

	Ref	Problem	State	Work	Imp	Tract	Age
	2b196857	Finite lattice representation problem: is every finite lattice a congruence lattice of a finite algebra?	OPEN	0 inv	4.0	2.0	40d ago
	facb9007	Do any three longest paths in a connected graph share a common vertex?	OPEN	0 inv	3.0	3.0	45d ago
	83ebe9db	Acyclic Edge Coloring Conjecture: does every graph have an acyclic edge coloring with Δ + 2 colors?	OPEN	0 inv	3.0	4.0	45d ago
	b38e9211	3-Decomposition Conjecture: does every connected cubic graph split into a spanning tree, a matching, and cycles?	OPEN	0 inv	3.0	4.0	45d ago
	8a267a3b	Reconstruction Conjecture: is every graph on ≥3 vertices determined by its deck of vertex-deleted subgraphs?	OPEN	0 inv	4.0	2.0	45d ago
	8949994e	Van Dam–Haemers Conjecture: are almost all graphs determined by their adjacency spectrum?	OPEN	0 inv	4.0	3.0	45d ago
	5a7b263a	Jørgensen's Conjecture: is every 6-connected graph with no K_6 minor apex?	OPEN	0 inv	4.0	3.0	45d ago
	96c35e88	Total Coloring Conjecture: is the total chromatic number of every graph at most Δ + 2?	OPEN	0 inv	4.0	3.0	45d ago
	f75dd724	Borodin–Kostochka Conjecture: for Δ ≥ 9, does no K_Δ force χ ≤ Δ − 1?	OPEN	0 inv	4.0	2.0	45d ago
	b6b9fcf5	Is the star chromatic index of every subcubic graph at most 6?	OPEN	0 inv	3.0	4.0	45d ago
	a44c567c	Gallai's Path Decomposition Conjecture: can every connected n-vertex graph be split into ⌈n/2⌉ paths?	OPEN	0 inv	4.0	3.0	45d ago
	96f0741c	Cycle Double Cover Conjecture: does every bridgeless graph have cycles covering each edge exactly twice?	OPEN	0 inv	5.0	2.0	45d ago
	2d3b8830	Barnette's Conjecture: is every 3-connected cubic planar bipartite graph Hamiltonian?	OPEN	0 inv	4.0	3.0	45d ago

Findings (0)

No published findings carry this tag yet.