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- Q5518852 subject Q7016011.
- Q5518852 subject Q7451460.
- Q5518852 subject Q7494515.
- Q5518852 abstract "In graph theory, the Gallai–Hasse–Roy–Vitaver theorem is a form of duality between the colorings of the vertices of a given undirected graph and the orientations of its edges. It states that a number k is the smallest number of colors among all colorings of graph G if and only if k is the largest number for which every orientation of G contains a simple directed path with k vertices. That is, the chromatic number is one plus the length of a longest path in an orientation of the graph chosen to minimize this path's length. The orientations for which the longest path has minimum length always include at least one acyclic orientation.An alternative statement of the same theorem is that every orientation of a graph with chromatic number k contains a simple directed path with k vertices; this path can be constrained to begin at any vertex that can reach all other vertices of the oriented graph.".
- Q5518852 thumbnail Gallai-Hasse-Roy-Vitaver_theorem.svg?width=300.
- Q5518852 wikiPageWikiLink Q1137726.
- Q5518852 wikiPageWikiLink Q1195339.
- Q5518852 wikiPageWikiLink Q131476.
- Q5518852 wikiPageWikiLink Q1320634.
- Q5518852 wikiPageWikiLink Q1475294.
- Q5518852 wikiPageWikiLink Q166507.
- Q5518852 wikiPageWikiLink Q174733.
- Q5518852 wikiPageWikiLink Q1755512.
- Q5518852 wikiPageWikiLink Q178377.
- Q5518852 wikiPageWikiLink Q2916352.
- Q5518852 wikiPageWikiLink Q3385162.
- Q5518852 wikiPageWikiLink Q45715.
- Q5518852 wikiPageWikiLink Q4677986.
- Q5518852 wikiPageWikiLink Q474715.
- Q5518852 wikiPageWikiLink Q504843.
- Q5518852 wikiPageWikiLink Q551830.
- Q5518852 wikiPageWikiLink Q622506.
- Q5518852 wikiPageWikiLink Q6874717.
- Q5518852 wikiPageWikiLink Q7016011.
- Q5518852 wikiPageWikiLink Q707119.
- Q5518852 wikiPageWikiLink Q7102401.
- Q5518852 wikiPageWikiLink Q719395.
- Q5518852 wikiPageWikiLink Q7227115.
- Q5518852 wikiPageWikiLink Q7451460.
- Q5518852 wikiPageWikiLink Q7494515.
- Q5518852 wikiPageWikiLink Q833449.
- Q5518852 wikiPageWikiLink Q917421.
- Q5518852 comment "In graph theory, the Gallai–Hasse–Roy–Vitaver theorem is a form of duality between the colorings of the vertices of a given undirected graph and the orientations of its edges. It states that a number k is the smallest number of colors among all colorings of graph G if and only if k is the largest number for which every orientation of G contains a simple directed path with k vertices.".
- Q5518852 label "Gallai–Hasse–Roy–Vitaver theorem".
- Q5518852 depiction Gallai-Hasse-Roy-Vitaver_theorem.svg.