Eulerian Graphs and Related TopicsEulerian Graphs and Related Topics |
Contents
| IR-1 | |
CHAPTER III BASIC CONCEPTS AND PRELIMINARY RESULTS | IR-27 |
CHAPTER IV CHARACTERIZATION THEOREMS AND COROLLARIES | IE-1 |
CHAPTER V EULER REVISITED AND AN OUTLOOK ON SOME GENERALIZATIONS | V-1 |
CHAPTER VI VARIOUS TYPES OF EULERIAN TRAILS | VE-1 |
CHAPTER VII TRANSFORMATIONS OF EULERIAN TRAILS | 175 |
| A-1 | |
| B-1 | |
Common terms and phrases
1-factor 2-connected 2-face-coloring 2-valent vertices 4-regular graph algorithm aneulerian arbitrary assume w.l.o.g. bd(F bieulerian bijection bipartite graph compatible eulerian trails conclude connected eulerian graph connected graph Consequently consider construction contains Corollary corresponding cubic graph cut set cut vertex cycle decomposition cycle H defined definition denote digraph edges elements embedded equivalent eulerian orientation eulerian triangulation Exercise exists face boundary face F Figure follows graph embedded graph G graph theory hamiltonian cycle hamiltonian path Hence implies induces a 2-splitting k-transformations kx-associates Let G mixed graph H Moreover NP-complete number of bridges obtain octahedron odd vertices Ot(v outerplane partition path perfect A-partition planar plane eulerian graph plane graph polynomial pontium precisely problem proof of Theorem result satisfies sequence Splitting Lemma strongly connected strongly connected component subgraph Suppose system of transitions Theorem VI.37 Theorem VII.10 trail of G transformation v e V(G vertices of G