Pancyclicity and NP-completeness in planar graphs

NP-completeness of the Planar Separator Problems

For a given graph G, the Separator Problem asks whether a vertex or edge set of small cardinality (or weight) exists whose removal partitions G into two disjoint graphs of approximately equal sizes. Called the Vertex Separator Problem when the removed set is a vertex set, and the Edge Separator Problem when it is an edge set, both problems are NP-complete for general unweighted graphs [6]. Desp...

NP-Completeness Results and Efficient Approximations for Radiocoloring in Planar Graphs

NP-completeness of list coloring and precoloring extension on the edges of planar graphs

In the edge precoloring extension problem we are given a graph with some of the edges having a preassigned color and it has to be decided whether this coloring can be extended to a proper k-edge-coloring of the graph. In list edge coloring every edge has a list of admissible colors, and the question is whether there is a proper edge coloring where every edge receives a color from its list. We s...

Panconnectedness and Pancyclicity in Graphs

with Local Ore-Type Conditions II A.S. Asratian, R H aggkvist and G.V. Sarkisian University of Ume a January, 1994 Abstract. It is well known due Ore that a graph G of order at least 3 is Hamiltonconnected if d(u) + d(v) jV (G)j + 1 for each pair of nonadjacent vertices u and v. We consider here connected graphs G of order at least 3 where d(u) + d(v) jN(u) [N(v) [N(w)j+ 1 for each triple of v...

A Generic Greedy Algorithm, Partially-Ordered Graphs and NP-Completeness