JCT
2007
13 years 11 months ago
2007
We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic orien...
JCT
2007
13 years 11 months ago
2007
An induced subgraph is called homogeneous if it is either a clique or an independent set. Let hom(G) denote the size of the largest homogeneous subgraph of a graph G. In this shor...
JCT
2007
13 years 11 months ago
2007
An edge in a drawing of a graph is called even if it intersects every other edge of the graph an even number of times. Pach and T´oth proved that a graph can always be redrawn so...
JCT
2007
13 years 11 months ago
2007
In [1] Johnson, Robertson, Seymour and Thomas define the notion of directed tree-width dtw(D) of a directed graph D. They ask whether dtw(D) ≥ k − 1 implies that D has a have...
JCT
2007
13 years 11 months ago
2007
JCT
2007
13 years 11 months ago
2007
A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a sim...
JCT
2007
13 years 11 months ago
2007
In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not who wins but rather how fast can one win. T...
JCT
2007
13 years 11 months ago
2007
We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. ...
JCT
2007
13 years 11 months ago
2007
JCT
2007
13 years 11 months ago
2007
Every finite, self-dual, regular (or chiral) 4-polytope of type {3, q, 3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we ob...