[PDF] Bipartite Graphs and Problem Solving
8 août 2007 · Theorem 2 4 If G is a k-regular bipartite graph with k > 0 and the bipartition of G is X and Y , then the number of elements in X is equal to the number of elements in Y deg(v) = k Y By the previous lemma, this means that k X = k Y =⇒ X = Y
[PDF] AN EDGE-COLORATION THEOREM FOR BIPARTITE GRAPH$ WI
An edge-coloration theorem for bipartite graphs, announced in [4], is proved from which some well-known theorems due to Kiinig [S] and the author [2, 31 are
[PDF] Lecture 1: Matchings on bipartite graphs 1 Basic Concepts
Theorem 2 3 We have (i) A minimal edge cover is minimum iff it contains a maximum matching (ii) A maximal matching is maximum
DENSITY THEOREMS FOR BIPARTITE GRAPHS AND RELATED
1 1 Ramsey numbers and density-type theorems for bipartite graphs Estimating and n≥2∆, there is a bipartite graph H with n vertices and maximum de-
[PDF] A RAMSEY-TYPE THEOREM FOR BIPARTITE GRAPHS Paul Erd
Any H-free graph with n vertices or its complement has a complete bi- partite subgraph with ⌊(n/k)1/(k−1)⌋ vertices in its classes The proof of Theorem 1 is
Decompositions bipartite graphs of regular - ScienceDirectcom
Theorem 3 5 Every 4-regular bipartite graph can be decomposed into 4-paths Pd In the proof we use a special case of the following
Cycles in Bipartite Graphs - ScienceDirect
then it contains a cycle of length 2a Theorem 1 is best possible in the following sense Consider a separable graph G(a, 2k - 1, k), with
[PDF] 3 Matchings
Theorem 3 2 (Hall's Marriage Theorem) Let G be a bipartite graph with bipartition (A, B) Then, there is a matching M ⊆ G which covers A if and only if
[PDF] BIPARTITE MINORS 1 Introduction Wagners celebrated theorem [5
of Wagner's theorem: a bipartite graph is planar if and only if it does not contain As bipartite planar graphs with n ≥ 3 vertices have at most 2n − 4 edges, and
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