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Fully decomposable split graphs
, 2009
"... We discuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable. ..."
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We discuss various questions around partitioning a split graph into connected parts. Our main result is a polynomial time algorithm that decides whether a given split graph is fully decomposable.
Integral Complete Split Graphs
"... We give characterizations of integral graphs in the family of complete split graphs and a few related families of graphs. ..."
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We give characterizations of integral graphs in the family of complete split graphs and a few related families of graphs.
On the EdgeColoring of Split Graphs
, 1996
"... We consider the following question: can split graphs with odd maximum degree be edgecoloured with maximum degree colours? We show that any odd maximum degree split graph can be transformed into a special split graph. For this special split graph, we were able to solve the question, in case the grap ..."
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We consider the following question: can split graphs with odd maximum degree be edgecoloured with maximum degree colours? We show that any odd maximum degree split graph can be transformed into a special split graph. For this special split graph, we were able to solve the question, in case
Absolute retracts of split graphs
"... It is proved that a split graph is an absolute retract of split graphs if and only if a partition of its vertex set into a stable set and a complete set is unique or it is a complete split graph. Three equivalent conditions for a split graph to be an absolute retract of the class of all graphs are ..."
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It is proved that a split graph is an absolute retract of split graphs if and only if a partition of its vertex set into a stable set and a complete set is unique or it is a complete split graph. Three equivalent conditions for a split graph to be an absolute retract of the class of all graphs
Dynamically maintaining split graphs
, 2007
"... We present an algorithm that supports operations for modifying a split graph by adding edges or vertices and deleting edges, such that after each modification the graph is repaired to become a split graph in a minimal way. In particular, if the graph is not split after the modification, the algorith ..."
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We present an algorithm that supports operations for modifying a split graph by adding edges or vertices and deleting edges, such that after each modification the graph is repaired to become a split graph in a minimal way. In particular, if the graph is not split after the modification
Containment relations in split graphs
, 2012
"... a b s t r a c t A graph containment problem is to decide whether one graph can be modified into some other graph by using a number of specified graph operations. We consider edge deletions, edge contractions, vertex deletions and vertex dissolutions as possible graph operations permitted. By allowi ..."
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. By allowing any combination of these four operations we capture the following ten problems: testing on (induced) minors, (induced) topological minors, (induced) subgraphs, (induced) spanning subgraphs, dissolutions and contractions. A split graph is a graph whose vertex set can be partitioned into a clique
Matrix Partitions of Split Graphs
"... Abstract Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split graphs. Previously such a result was only known for ..."
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Abstract Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split graphs. Previously such a result was only known
RECOGNIZING PERFECT 2SPLIT GRAPHS
, 2000
"... A graph is a split graph if its vertices can be partitioned into a clique and a stable set. A graph is a ksplit graph if its vertices can be partitioned into k sets, each of which induces a split graph. We show that the strong perfect graph conjecture is true for 2split graphs and we design a poly ..."
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Cited by 5 (0 self)
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A graph is a split graph if its vertices can be partitioned into a clique and a stable set. A graph is a ksplit graph if its vertices can be partitioned into k sets, each of which induces a split graph. We show that the strong perfect graph conjecture is true for 2split graphs and we design a
Counting Set Covers and Split Graphs
, 2000
"... A bijection between split graphs and minimal covers of a set by subsets is presented. As the enumeration problem for such minimal covers has been solved, this implies that split graphs can also be enumerated. ..."
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A bijection between split graphs and minimal covers of a set by subsets is presented. As the enumeration problem for such minimal covers has been solved, this implies that split graphs can also be enumerated.
Results 1  10
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1,295