Note on transformations of posets with the same upper bound graph and minimal elements.
Old and new generalizations of line graphs.
On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs
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 linear layouts of graphs.
On metro-line crossing minimization.
On rational radii coin representations of the wheel graph
A flower is a coin graph representation of the wheel graph. A petal of a flower is an outer coin connected to the center coin. The results of this paper are twofold. First we derive a parametrization of all the rational (and hence integer) radii coins of the 3-petal flower, also known as Apollonian circles or Soddy circles. Secondly we consider a general n-petal flower and show there is a unique irreducible polynomial Pₙ in n variables over the rationals ℚ, the affine variety of which contains the...
On recognition of strong graph bundles
On recursively directed hypercubes.
On the graphs of Hoffman-Singleton and Higman-Sims.
On the perspectives opened by right angle crossing drawings.
Orientation distance graphs revisited
The orientation distance graph 𝓓ₒ(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to existing results, especially with regards to the bipartiteness of orientation distance graphs and the representation...
Orthogonal drawings of plane graphs without bends.
Outerplanar crossing numbers, the circular arrangement problem and isoperimetric functions.
Path, trail and walk graphs.
Planar decompositions and the crossing number of graphs with an excluded minor.
Planar drawings of higher-genus graphs.
Polar coordinate drawing of planar graphs with good angular resolution.
Quartet compatibility and the quartet graph.
Queue layouts of graph products and powers.
Rainbow Tetrahedra in Cayley Graphs
Let Γn be the complete undirected Cayley graph of the odd cyclic group Zn. Connected graphs whose vertices are rainbow tetrahedra in Γn are studied, with any two such vertices adjacent if and only if they share (as tetrahedra) precisely two distinct triangles. This yields graphs G of largest degree 6, asymptotic diameter |V (G)|1/3 and almost all vertices with degree: (a) 6 in G; (b) 4 in exactly six connected subgraphs of the (3, 6, 3, 6)-semi- regular tessellation; and (c) 3 in exactly four connected...