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A note on mixed graphs and directed splitting off
Author(s) -
Enni Steffen
Publication year - 1998
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199804)27:4<213::aid-jgt2>3.0.co;2-q
Subject(s) - mathematics , combinatorics , eulerian path , counterexample , conjecture , vertex (graph theory) , directed graph , discrete mathematics , arc (geometry) , comparability graph , mixed graph , graph , pathwidth , line graph , voltage graph , pure mathematics , lagrangian , geometry
We give counterexamples to two conjectures of Bill Jackson in Some remarks on arc‐connectivity, vertex splitting, and orientation in graphs and digraphs ( Journal of Graph Theory 12 (3):429–436, 1988) concerning orientations of mixed graphs and splitting off in digraphs, and prove the first conjecture in the (di‐) Eulerian case(s). Beside that we solve a degree constrained non‐uniform directed augmentation problem for di‐Eulerian mixed graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 213–221, 1998