Algebraic properties of edge ideals via combinatorial topology.
Dochtermann, Anton, Engström, Alexander (2009)
The Electronic Journal of Combinatorics [electronic only]
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Dochtermann, Anton, Engström, Alexander (2009)
The Electronic Journal of Combinatorics [electronic only]
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Idzik, Adam, Zapart, Anna (2010)
Fixed Point Theory and Applications [electronic only]
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Marietti, Mario, Testa, Damiano (2008)
The Electronic Journal of Combinatorics [electronic only]
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Ralf Fröberg (1990)
Banach Center Publications
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Berglund, Alexander (2009)
The Electronic Journal of Combinatorics [electronic only]
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Choi, Suyoung, Kim, Jang Soo (2010)
The Electronic Journal of Combinatorics [electronic only]
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Endre Boros, Robert E. Jamison, Renu Laskar, Henry Martyn Mulder (2004)
Discussiones Mathematicae Graph Theory
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A vertex v in a graph G = (V,E) is k-simplicial if the neighborhood N(v) of v can be vertex-covered by k or fewer complete graphs. The main result of the paper states that a planar graph of order at least four has at least four 3-simplicial vertices of degree at most five. This result is a strengthening of the classical corollary of Euler's Formula that a planar graph of order at least four contains at least four vertices of degree at most five.
Bohdan Zelinka (1973)
Kybernetika
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Goldberg, Mark K., Magdon-Ismail, Malik (2011)
The Electronic Journal of Combinatorics [electronic only]
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Murai, Satoshi (2009)
The Electronic Journal of Combinatorics [electronic only]
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M. R. Casali (1997)
Revista Matemática de la Universidad Complutense de Madrid
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Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.