On the Maximum Diameter of $k$-Colorable Graphs

Approximating maximum weight K-colorable subgraphs in chordal graphs

We present a 2-approximation algorithm for the problem of finding the maximum weight K-colorable subgraph in a given chordal graph with node weights. The running time of the algorithm is O(K(n+m)), where n and m are the number of vertices and edges in the given graph.

On disjoint matchings in cubic graphs: Maximum 2-edge-colorable and maximum 3-edge-colorable subgraphs

We show that any 2−factor of a cubic graph can be extended to a maximum 3−edge-colorable subgraph. We also show that the sum of sizes of maximum 2− and 3−edge-colorable subgraphs of a cubic graph is at least twice of its number of vertices.

Bipartite, k-Colorable and k-Colored Graphs

ON GENERALIZED k-DIAMETER OF k-REGULAR k-CONNECTED GRAPHS

In this paper, motivated by the study of the wide diameter and the Rabin number of graphs, we define the generalized k-diameter of k-connected graphs, and show that every k-regular k-connected graph on n vertices has the generalized k-diameter at most n/2 and this upper bound cannot be improved when n = 4k − 6 + i(2k − 4).

Coloring k-colorable graphs using smaller palettes

We obtain the following new coloring results: A 3-colorable graph on n vertices with maximum degree can be colored, in polynomial time, us