Inductive $$k$$ k -independent graphs and c-colorable subgraphs in scheduling: a review

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.

Bipartite, k-Colorable and k-Colored Graphs

On spanning $k$-edge-colorable subgraphs

A subgraph H of a multigraph G is called strongly spanning, if any vertex of G is not isolated in H , while it is called maximum k-edge-colorable, if H is proper k-edge-colorable and has the largest size. We introduce a graph-parameter sp(G), that coincides with the smallest k that a graph G has a strongly spanning maximum k-edge-colorable subgraph. Our first result offers some alternative defi...

ON STRONGLY SPANNING k-EDGE-COLORABLE SUBGRAPHS

A subgraph H of a multigraph G is called strongly spanning, if any vertex of G is not isolated in H. H is called maximum k-edge-colorable, if H is proper k-edge-colorable and has the largest size. We introduce a graph-parameter sp(G), that coincides with the smallest k for which a multigraph G has a maximum k-edge-colorable subgraph that is strongly spanning. Our first result offers some altern...

Algorithms for cliques in inductive k-independent graphs

A graph is inductive k-independent if there exists an ordering of its vertices v1, ..., vn such that α(G[N(vi)∩Vi]) ≤ k where N(vi) is the neighbourhood of vi, Vi = {vi, ..., vn} and α is the independence number. In this article we design a polynomial time approximation algorithm with ratio ∆/ log(log(∆)/(k+1)) for the maximum clique problem and also show that the decision version of this probl...