Results 11 to 20 of about 1,282,765 (250)
Weak Degeneracy of Planar Graphs and Locally Planar Graphs [PDF]
The Electronic Journal of Combinatorics, 2023 Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d+1)$-list assignment $L$ of $G$, one can construct an $L$ coloring of $G$ by a modified ...
Ming Han +4 more
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Discrete Mathematics, 1974 AbstractA 3-valent graph G is cyclically n-connected provided one must cut at least n edges in order to separate any two circuits of G. If G is cyclically n-connected but any separation of G by cutting n edges yields a component consisting of a simple circuit, then we say that G is strongly cyclically n-connected.
David Barnette
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Historia Mathematica, 1985 In 1930 \textit{K. Kuratowski} published a proof of the ''Theorem on planar graphs'': A graph is planar if and only if it does not contain a subgraph homeomorphic to either \(K_ 5\) (the complete graph on 5 points), or \(K_{3,3}\) (the complete bipartite graph on 3,3 points).
John W. Kennedy +2 more
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A theorem on planar graphs [PDF]
Transactions of the American Mathematical Society, 1956 W. T. Tutte
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The Odd Chromatic Number of a Planar Graph is at Most 8 [PDF]
Graphs and Combinatorics, 2022 Petruševski and Škrekovski recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph G is said to be odd if for each non-isolated vertex $$x \in V(G)$$ x ∈ V ( G ) there exists a colour c appearing an odd number ...
J. Petr, Julien Portier
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The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
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An improved planar graph product structure theorem [PDF]
Electronic Journal of Combinatorics, 2021 Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph $G$ there is a graph $H$ with treewidth at most 8 and a path $P$ such that $G\subseteq H\boxtimes P$. We improve this result by replacing "treewidth at most
T. Ueckerdt, D. Wood, Wendy Yi
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Improved product structure for graphs on surfaces [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel +3 more
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Shallow Minors, Graph Products, and Beyond-Planar Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2021 The planar graph product structure theorem of Dujmovi\'{c}, Joret, Micek, Morin, Ueckerdt, and Wood [J. ACM 2020] states that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path.
Robert Hickingbotham, D. Wood
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Quantum approximate optimization of non-planar graph problems on a planar superconducting processor [PDF]
Nature Physics, 2020 Faster algorithms for combinatorial optimization could prove transformative for diverse areas such as logistics, finance and machine learning. Accordingly, the possibility of quantum enhanced optimization has driven much interest in quantum technologies.
F. Arute +83 more
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