论文信息 - On the chordality of a graph

On the chordality of a graph

The chordality of a graph G = (V, E) is defined as the minimum k such that we can write E = E1 ∩ … ∩ Ek with each (V, Ei) a chordal graph. We present several results bounding the value of this generalization of boxicity. Our principal result is that the chordality of a graph is at most its tree width. In particular, series-parallel graphs have chordality at most 2. Potential strengthenings of this statement fail in that there are planar graphs with chordality 3 and series-parallel graphs with boxicity 3. © 1993 John Wiley & Sons, Inc.

Terry A. McKee | Edward R. Scheinerman | T. McKee | E. Scheinerman

[1] Donald J. ROSE,et al. On simple characterizations of k-trees , 1974, Discret. Math..

[2] Carsten Thomassen,et al. Interval representations of planar graphs , 1986, J. Comb. Theory, Ser. B.

[3] G. Dirac. A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs , 1952 .

[4] James R. Walter,et al. Representations of chordal graphs as subtrees of a tree , 1978, J. Graph Theory.

[5] F. Gavril. The intersection graphs of subtrees in tree are exactly the chordal graphs , 1974 .

[6] Peter Buneman,et al. A characterisation of rigid circuit graphs , 1974, Discret. Math..

[7] R. Duffin. Topology of series-parallel networks , 1965 .

[8] M. Golumbic. Algorithmic graph theory and perfect graphs , 1980 .

[9] R. E. Pippert,et al. Properties and characterizations of k -trees , 1971 .

[10] Fred S. Roberts,et al. On dimensional properties of graphs , 1989, Graphs Comb..

[11] Paul D. Seymour,et al. Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.