On biembeddings of Latin squares.
On chirality groups and regular coverings of regular oriented hypermaps
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.
On cyclically embeddable graphs
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.
On doubly light vertices in plane graphs
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
On face-vectors and vertex-vectors of polyhedral maps on orientable -manifolds
On generalized outerplanarity of line graphs
On homotopical equivalence of tolerance spaces
On infinite outerplanar graphs
In this Note, we study infinite graphs with locally finite outerplane embeddings, given a characterization by forbidden subgraphs.
On light subgraphs in plane graphs of minimum degree five
A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is well known that a plane graph of minimum degree five contains light edges and light triangles. In this paper we show that every plane graph of minimum degree five contains also light stars and and a light 4-path P₄. The results obtained for and P₄ are best possible.
On linear layouts of graphs.
On local properties of graphs again
On local structure of 1-planar graphs of minimum degree 5 and girth 4
A graph is 1-planar if it can be embedded in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree 5 and girth 4 contains (1) a 5-vertex adjacent to an ≤ 6-vertex, (2) a 4-cycle whose every vertex has degree at most 9, (3) a with all vertices having degree at most 11.
On locally quasiconnected graphs and their upper embeddability
On Longest Cycles in Essentially 4-Connected Planar Graphs
A planar 3-connected graph G is essentially 4-connected if, for any 3-separator S of G, one component of the graph obtained from G by removing S is a single vertex. Jackson and Wormald proved that an essentially 4-connected planar graph on n vertices contains a cycle C such that [...] . For a cubic essentially 4-connected planar graph G, Grünbaum with Malkevitch, and Zhang showed that G has a cycle on at least ¾ n vertices. In the present paper the result of Jackson and Wormald is improved. Moreover,...
On magic labellings of type for three classes of plane graphs
On metro-line crossing minimization.
On non-separating embeddings of graphs in closed surfaces.