[PDF] Top 20 Clique graphs of chordal and path graphs

... Different characterizations of expanded trees are described, leading to a polynomial time algorithm for rccognizing clique graphs of chordal and path graphs.... A sp[r] ... See full document

... representation of large graphs. Power graphs serve as a novel represen- tation that uses cliques, bicliques, and stars as primitives, thus reducing the number of original nodes ... See full document

... number of graphs in any class without large connected induced bipartite ...free graphs is α-polynomial, where CONNBIP ( ) N is the set of all connected bipartite graphs of order ... See full document

... incident of a catastrophic disaster of the Korean Air Lines Flight 007, where 267 air passengers died (Times, ...result of that, the GPS technology has been released by former US president Ronald ... See full document

... (the clique number ω(G)) of a graph G is the maximal order of a co-clique ...(resp. clique) contained in G as an induced subgraph (note that a co-clique and clique ... See full document

... vertices of degree one, and a caterpillar is a tree that can be converted into a path or a single vertex by deleting all vertices of degree ... See full document

... [5] studied the complexity of the more general problem of partitioning a graph in dense and sparse subgraphs (independent sets induce sparse graphs and cliques induce d[r] ... See full document

... the path Q we obtain c disjoint paths; these paths and Q are induced paths that do not intersect and that cover all vertices of ...loss of generality, that v ∈ S P (H) . Then each ... See full document

... (Note that in this case we need no restriction to chordal graphs. ) The value of the algorithm is underscored by the fact that it easily adapts to solve the list[r] ... See full document

... structure of the problem undergoes changes, rather than computing an entirely new solution from ...sequence of intermixed updates and queries: an update inserts or deletes an edge or isolated vertex ... See full document

... Lemma 1. We shall prove that, in fact, the neighborhoods of the vertices of C in C' are linearly ordered. The lemma follows by taking the vertex in C with maximal n[r] ... See full document

... connected chordal graph G (Theorem ...help of Lemma ...for chordal graphs, we use a corresponding clique tree of the graph (that is, a tree decomposition as in Proposition ... See full document

... background and prehistory for this paper goes something like the ...notion of independence for columns (rows) of as matrix with coefficients in a supertropical ...2.4), and then to the subset ... See full document

... truth-value of a variable is flipped (i.e., complemented), the total number of satisfied clauses will ...number of such clauses is represented by ...number of such clauses is given by ... See full document

... study of proofs from a geometric perspective one can hardly overestimate the pioneering work of Statman in his doctoral thesis Structural Complexity of Proofs (STATMAN, ...study of structural ... See full document

... outline of the ...sharp and improved upper bound for the energy of bipartite graphs and for large family of graphs, namely those graphs whose adjacency matrix is ... See full document

... some of these bounds are already known, so, as is evident, we studied the unknown ...class of triangulations, namely the maximal outerplanar graphs; and concerning the distance versions we ... See full document

... graphs with given nullity and minimum energy. When we compare the lower bound in (??) with the lower bound in (??), the arithmetic difference of the second one minus the first one gives ρ − 1 + ln ρ ... See full document

... subset of edges, M  E.G/; no two of which have a common ...edge of the matching M incident with i; then M is called a perfect ...determination of a maximum stable set of a line graph, ... See full document

... structure of communities in the ...statistics of the graph, for example, the number of edges, the number of triangles, the number of stars, and so ...lot of attention from ... See full document