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Displaying similar documents to “A new approach to chordal graphs”

An algebraic characterization of geodetic graphs

Ladislav Nebeský (1998)

Czechoslovak Mathematical Journal

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We say that a binary operation * is associated with a (finite undirected) graph G (without loops and multiple edges) if * is defined on V ( G ) and u v E ( G ) if and only if u v , u * v = v and v * u = u for any u , v V ( G ) . In the paper it is proved that a connected graph G is geodetic if and only if there exists a binary operation associated with G which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).

On signpost systems and connected graphs

Ladislav Nebeský (2005)

Czechoslovak Mathematical Journal

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By a signpost system we mean an ordered pair ( W , P ) , where W is a finite nonempty set, P W × W × W and the following statements hold: if ( u , v , w ) P , then ( v , u , u ) P and ( v , u , w ) P , for all u , v , w W ; if u v , i then there exists r W such that ( u , r , v ) P , for all u , v W . We say that a signpost system ( W , P ) is smooth if the folowing statement holds for all u , v , x , y , z W : if ( u , v , x ) , ( u , v , z ) , ( x , y , z ) P , then ( u , v , y ) P . We say thay a signpost system ( W , P ) is simple if the following statement holds for all u , v , x , y W : if ( u , v , x ) , ( x , y , v ) P , then ( u , v , y ) , ( x , y , u ) P . By the underlying graph of a signpost system ( W , P ) we mean the graph G with V ( G ) = W and such that the following statement holds for all distinct u , v W : u and v are adjacent in G if and...

The induced paths in a connected graph and a ternary relation determined by them

Ladislav Nebeský (2002)

Mathematica Bohemica

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By a ternary structure we mean an ordered pair ( X 0 , T 0 ) , where X 0 is a finite nonempty set and T 0 is a ternary relation on X 0 . By the underlying graph of a ternary structure ( X 0 , T 0 ) we mean the (undirected) graph G with the properties that X 0 is its vertex set and distinct vertices u and v of G are adjacent if and only if { x X 0 T 0 ( u , x , v ) } { x X 0 T 0 ( v , x , u ) } = { u , v } . A ternary structure ( X 0 , T 0 ) is said to be the B-structure of a connected graph G if X 0 is the vertex set of G and the following statement holds for all u , x , y X 0 : T 0 ( x , u , y ) if and only if u belongs to an...