Orientations of circle graphs

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

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

Distances in orientations of graphs

✍ V Chvátal; C Thomassen 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 815 KB

Recognition of Circle Graphs

✍ J. Spinrad 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 736 KB

This paper presents a new algorithm for recognizing circle graphs, combining ideas from an earlier circle graph recognition algorithm due to Gabor, Hsu, and Supowit and an algorithm to determine whether a graph can be decomposed by the split decomposition. The result is an \(O\left(n^{2}\right)\) al

Two-connected orientations of Eulerian g

Two-connected orientations of Eulerian graphs

✍ Alex R. Berg; Tibor Jordán 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 116 KB

## Abstract A graph __G__ = (__V__, __E__) is said to be weakly four‐connected if __G__ is 4‐edge‐connected and __G__ – __x__ is 2‐edge‐connected for every __x__ ∈ __V__. We prove that every weakly four‐connected Eulerian graph has a 2‐connected Eulerian orientation. This verifies a special case of

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