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Mathematical Notes, 2021
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Grigoryan, Alexander +2 more
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Grigoryan, Alexander +2 more
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Journal of Graph Theory, 2014
AbstractThe clique number of a digraph D is the size of the largest bidirectionally complete subdigraph of D. D is perfect if, for any induced subdigraph H of D, the dichromatic number defined by Neumann‐Lara (The dichromatic number of a digraph, J. Combin. Theory Ser. B 33 (1982), 265–270) equals the clique number .
Stephan Dominique Andres +1 more
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AbstractThe clique number of a digraph D is the size of the largest bidirectionally complete subdigraph of D. D is perfect if, for any induced subdigraph H of D, the dichromatic number defined by Neumann‐Lara (The dichromatic number of a digraph, J. Combin. Theory Ser. B 33 (1982), 265–270) equals the clique number .
Stephan Dominique Andres +1 more
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Regular Digraphs Containing a Given Digraph
Canadian Mathematical Bulletin, 1984AbstractLet the maximum degree d of a digraph D be the maximum of the set of all outdegrees and indegrees of the points of D. We prove that every digraph D of order P and maximum degree d has a d-regular superdigraph H with at most d + 1 more points, and that this bound, which is independent of p, is best possible.
Harary, Frank, Karabed, Razmik
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On super‐edge‐connected digraphs and bipartite digraphs
Journal of Graph Theory, 1992AbstractA maximally edge‐connected digraph is called super‐λ if every minimum edge disconnecting set is trivial, i.e., it consists of the edges adjacent to or from a given vertex. In this paper sufficient conditions for a digraph to be super‐λ are presented in terms of parameters such as diameter and minimum degree.
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CKI-Digraphs, Generalized Sums and Partitions of Digraphs
Graphs and Combinatorics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hortensia Galeana-Sánchez, Mika Olsen
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Discrete Applied Mathematics
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Marisa Gutierrez +3 more
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Marisa Gutierrez +3 more
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SIAM Journal on Discrete Mathematics, 2010
One of the classical results in packing theory states that every graph of order $n$ and size less than or equal to $n-2$ is packable in its complement. Moreover, the bound is sharp because the star is not packable. A similar problem arises for digraphs, namely, to find the maximal number $f_D(n)$ such that every digraph of order $n$ and size less than ...
Agnieszka Görlich, Andrzej Zak
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One of the classical results in packing theory states that every graph of order $n$ and size less than or equal to $n-2$ is packable in its complement. Moreover, the bound is sharp because the star is not packable. A similar problem arises for digraphs, namely, to find the maximal number $f_D(n)$ such that every digraph of order $n$ and size less than ...
Agnieszka Görlich, Andrzej Zak
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Canadian Mathematical Bulletin, 1966
The line - graph of an ordinary graph G is that graph whose points can be put in one-to-one correspondence with the lines of G in such a way that two points of are adjacent if and only if the corresponding lines of G are adjacent. This concept originated with Whitney [ 5 ], has the property that its (point) chromatic number equals the line chromatic
Chartrand, G., Stewart, M. J.
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The line - graph of an ordinary graph G is that graph whose points can be put in one-to-one correspondence with the lines of G in such a way that two points of are adjacent if and only if the corresponding lines of G are adjacent. This concept originated with Whitney [ 5 ], has the property that its (point) chromatic number equals the line chromatic
Chartrand, G., Stewart, M. J.
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Canadian Journal of Mathematics, 1967
SummaryWe call a digraph “antisymmetrical” if there is an automorphismθof its graph, of period 2, which reverses the direction of every edge and maps no edge or vertex onto itself. We construct a theory of flows invariant underθfor such a diagraph. This theory is analogous to the Max Flow Min Cut theory for ordinary flows in digraphs.
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SummaryWe call a digraph “antisymmetrical” if there is an automorphismθof its graph, of period 2, which reverses the direction of every edge and maps no edge or vertex onto itself. We construct a theory of flows invariant underθfor such a diagraph. This theory is analogous to the Max Flow Min Cut theory for ordinary flows in digraphs.
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Acta Mathematica Scientia, 1988
The paper shows that a digraph is a posetable digraph if and only if by removing any arc (u,v) from the digraph, the resulting digraph contains no directed path between u and v.
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The paper shows that a digraph is a posetable digraph if and only if by removing any arc (u,v) from the digraph, the resulting digraph contains no directed path between u and v.
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