Distances in orientations of graphs

Orientation distance graphs

✍ Gary Chartrand; David Erwin; Michael Raines; Ping Zhang 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 194 KB

For two nonisomorphic orientations D and D H of a graph G, the orientation distance d o (D,D H ) between D and D H is the minimum number of arcs of D whose directions must be reversed to produce an orientation isomorphic to D H . The orientation distance graph h o (G) of G has the set y(G) of pairwi

Acyclic orientations of graphs

✍ Richard P. Stanley 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 708 KB

## Let G be a finite graph with p vertices and x its chromatic polynomial. A combinatorial interpretation is given to the positive integer (-l)px(-A), where h is a positive integer, in terms of acyclic orientations of G. In particular, (-l)Px(-1) is the number of acyclic orientations of G. An appl

Orientations of circle graphs

✍ R. C. Read; D. Rotem; J. Urrutia 📂 Article 📅 1982 🏛 John Wiley and Sons 🌐 English ⚖ 756 KB

Sinks in Acyclic Orientations of Graphs

✍ David D. Gebhard; Bruce E. Sagan 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 183 KB

Greene and Zaslavsky proved that the number of acyclic orientations of a graph G with a unique sink at a given vertex is, up to sign, the linear coefficient of the chromatic polynomial. We give three proofs of this result using pure induction, noncommutative symmetric functions, and an algorithmic b

Orientations of graphs in kernel theory

✍ H. Galeana-Sánchez; V. Neumann-Lara 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 589 KB

In this paper we investigate structural properties of a certain class of graphs (%&free graphs) which are relevant in the study of kernel theory, m-free graphs satisfy the strong perfect graph conjecture of Berge. We investigate orientations of Z&free graphs and other classes of graphs which produce

Acyclic Orientations of Random Graphs

✍ C.M Reidys 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 195 KB

An acyclic orientation of an undirected graph is an orientation of its edges such that the resulting directed graph contains no cycles. The random graph G is a n, p probability space consisting of subgraphs of K that are obtained by selecting each n K -edge with independent probability p. The random