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Octonion multiplication and Heawood’s map
Bruno Sévennec (2013)
Confluentes Mathematici
In this note, the octonion multiplication table is recovered from a regular tesselation of the equilateral two timensional torus by seven hexagons, also known as Heawood’s map.
On 2-cell embeddings of graphs with minimum numbers of regions
Ladislav Nebeský (1985)
Czechoslovak Mathematical Journal
On 2-cell imbeddings of complete n-partite graphs
H. V. Kronk, R. D. Ringeisen, A. T. White (1976)
Colloquium Mathematicae
On 3-simplicial vertices in planar graphs
Endre Boros, Robert E. Jamison, Renu Laskar, Henry Martyn Mulder (2004)
Discussiones Mathematicae Graph Theory
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.
On a certain class of polytopes associated with independence systems.
A.B. Hansen (1977)
Mathematica Scandinavica
On a certain distance between isomorphism classes of graphs
Bohdan Zelinka (1975)
Časopis pro pěstování matematiky
On a matching distance between rooted phylogenetic trees
Damian Bogdanowicz, Krzysztof Giaro (2013)
International Journal of Applied Mathematics and Computer Science
The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs, the values...
On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs
Július Czap, Jakub Przybyło, Erika Škrabuľáková (2016)
Discussiones Mathematicae Graph Theory
A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets. Bipartite 1-planar graphs are known to have at most 3n − 8 edges, where n denotes the order of a graph. We show that maximal-size bipartite 1-planar graphs which are almost balanced have not significantly fewer edges than indicated by this upper bound, while the same is not true...
On biembeddings of Latin squares.
Grannell, M.J., Griggs, T.S., Knor, M. (2009)
The Electronic Journal of Combinatorics [electronic only]
On chirality groups and regular coverings of regular oriented hypermaps
Antonio Breda d'Azevedo, Ilda Inácio Rodrigues, Maria Elisa Fernandes (2011)
Czechoslovak Mathematical Journal
We prove that if the Walsh bipartite map of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps induced by the family of toroidal bipartite maps...
On cubic planar hypohamiltonian and hypotraceable graphs.
Araya, Makoto, Wiener, Gábor (2011)
The Electronic Journal of Combinatorics [electronic only]
On cyclically embeddable graphs
Mariusz Woźniak (1999)
Discussiones Mathematicae Graph Theory
An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.
On double coverings of some rotary hypermaps.
Breda, Ana, d'Azevedo, Antonio Breda, Catalano, Domenico (2009)
Beiträge zur Algebra und Geometrie
On doubly light vertices in plane graphs
Veronika Kozáková, Tomáš Madaras (2011)
Discussiones Mathematicae Graph Theory
A vertex is said to be doubly light in a family of plane graphs if its degree and sizes of neighbouring faces are bounded above by a finite constant. We provide several results on the existence of doubly light vertices in various families of plane graph.
On Eggleton and Guy’s conjectured upper bound for the crossing number of the -cube
Luerbio Faria, Celina Miraglia Herrera de Figueiredo (2000)
Mathematica Slovaca
On face-vectors and vertex-vectors of polyhedral maps on orientable -manifolds
Stanislav Jendroľ (1993)
Mathematica Slovaca
On generalized outerplanarity of line graphs
Jiří Sedláček (1990)
Časopis pro pěstování matematiky
On homotopical equivalence of tolerance spaces
Jaromír Šiška (1978)
Commentationes Mathematicae Universitatis Carolinae
On infinite outerplanar graphs
Luis B. Boza, Ana Diánez, Alberto Márquez (1994)
Mathematica Bohemica
In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden subgraphs.
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