JGT
2007
13 years 4 months ago
2007
Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-fa...
JGT
2007
13 years 4 months ago
2007
JGT
2007
13 years 4 months ago
2007
JGT
2007
13 years 4 months ago
2007
We demonstrate four intrinsically knotted graphs that do not contain each other, nor any previously known intrinsically knotted graph, as a minor.
JGT
2007
13 years 4 months ago
2007
A graph G is a quasi-line graph if for every vertex v, the set of neighbors of v can be expressed as the union of two cliques. The class of quasi-line graphs is a proper superset ...
JGT
2007
13 years 4 months ago
2007
JGT
2007
13 years 4 months ago
2007
A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same face have distinct colours. The minimum number of colours in a cyclic colouring...
JGT
2007
13 years 4 months ago
2007
JGT
2007
13 years 4 months ago
2007
A 3-uniform hypergraph is called a minimum 3-tree, if for any 3-coloring of its vertex set there is a heterochromatic triple and the hypergraph has the minimum possible number of ...
JGT
2007
13 years 4 months ago
2007
Laman’s characterization of minimally rigid 2-dimensional generic frameworks gives a matroid structure on the edge set of the underlying graph, as was first pointed out and expl...