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Description
  • In the project, we will consider two important problems in the field of Graph Theory: (i) rainbow colouring of graphs, especially computation of (or at least bounds for) the rainbow connection number rc(G) of a given graph G – the problem has an interesting application for the secure transfer of classified information between agencies in communication networks; (ii) computation of (or at least bounds for the size of) a largest subgraph with prescribed properties – cycle, path, trestle (a spanning 2-connected subgraph of bounded degree) etc. – knowledge about such subgraphs has major importance on the structure of a given graph and its other graph properties. (en)
  • V projektu se budeme zabývat dvěma důležitými problémy teorie grafů: (i) duhové barvení grafů, zejména určení (či odhady) duhového čísla souvislosti rc(G) daného grafu G – problém má aplikace pro bezpečný přenos informací mezi agenturami v komunikačních sítích; (ii) nalezení (či odhady velikosti) největšího podgrafu daných vlastností – kružnice, cesty, trestle (2-souvislého faktoru s omezeným maximálním stupněm) atd. v daném (konečném) grafu – znalost těchto podgrafů má významnou roli pro strukturu daného grafu a jeho další grafové vlastnosti.
Title
  • Rainbow connection and cycles in graphs (en)
  • Duhová souvislost a cykly v grafech
skos:notation
  • 7AMB13DE003
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  • edge colouring, rainbow connection, longest cycle, hamiltonicity, trestle (en)
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  • hamiltonicity
  • longest cycle
  • rainbow connection
  • edge colouring
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