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Results 1 - 10
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200
Contractible Cliques in k-Connected Graphs
, 2005
"... Kawarabayashi proved that for any integer k ≥ 4, every k-connected graph contains two triangles sharing an edge, or admits a k-contractible edge, or admits a k-contractible triangle. This implies Thomassen’s result that every triangle-free k-connected graph contains a k-contractible edge. In this pa ..."
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Kawarabayashi proved that for any integer k ≥ 4, every k-connected graph contains two triangles sharing an edge, or admits a k-contractible edge, or admits a k-contractible triangle. This implies Thomassen’s result that every triangle-free k-connected graph contains a k-contractible edge
Contractible Subgraphs in k-Connected Graphs
, 2006
"... For a graph G we define a graph T(G) whose vertices are the triangles in G and two vertices of T(G) are adjacent if their corresponding triangles in G share an edge. Kawarabayashi showed that if G is a k-connected graph and T(G) contains no edge then G admits a k-contractible clique of size at most ..."
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For a graph G we define a graph T(G) whose vertices are the triangles in G and two vertices of T(G) are adjacent if their corresponding triangles in G share an edge. Kawarabayashi showed that if G is a k-connected graph and T(G) contains no edge then G admits a k-contractible clique of size at most
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is ffl-far from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 475 (67 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being k-colorable or having a ae-clique (clique of density ae
Note on k-contractible edges in k-connected graphs
"... It is proved that if G is a k-connected graph which does not contain K;; with k being odd, then G has an edge e such that the graph obtained from G by contracting e is still k-connected. The same conclusion does not hold when k is even. This result is a generalization of the famous theorem of Thomas ..."
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It is proved that if G is a k-connected graph which does not contain K;; with k being odd, then G has an edge e such that the graph obtained from G by contracting e is still k-connected. The same conclusion does not hold when k is even. This result is a generalization of the famous theorem
Clique-width and edge contraction
, 2013
"... We prove that edge contractions do not preserve the property that a set of graphs has bounded clique-width. ..."
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Cited by 1 (0 self)
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We prove that edge contractions do not preserve the property that a set of graphs has bounded clique-width.
Clique Minors In Graphs And Their Complements
, 2000
"... A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t ≥ 1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c = c(k) independent of G such that the complement of G h ..."
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Cited by 2 (0 self)
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A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t ≥ 1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c = c(k) independent of G such that the complement of G
Graphs of Power-Bounded Clique-Width
, 2014
"... Clique-width is a graph parameter with many algorithmic applications. For a positive integer k, the k-th power of a graph G is the graph with the same vertex set as G, in which two distinct vertices are adjacent if and only if they are at distance at most k in G. Many graph algorithmic problems can ..."
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classes of power-unbounded clique-width and give a sufficient condition for clique-width to be power-bounded. Based on this condition, we characterize graph classes of power-bounded clique-width among classes defined by two connected forbidden induced subgraphs. We also show that for every integer k
CLIQUE MINORS IN CARTESIAN PRODUCTS OF GRAPHS
, 2008
"... A clique minor in a graph G can be thought of as a set of connected subgraphs in G that are pairwise disjoint and pairwise adjacent. The Hadwiger number ηÔGÕis the maximum cardinality of a clique minor in G. This paper studies clique minors in the Cartesian product G¥H. Our main result is a rough s ..."
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Cited by 8 (6 self)
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A clique minor in a graph G can be thought of as a set of connected subgraphs in G that are pairwise disjoint and pairwise adjacent. The Hadwiger number ηÔGÕis the maximum cardinality of a clique minor in G. This paper studies clique minors in the Cartesian product G¥H. Our main result is a rough
Results 1 - 10
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200
