Proceedings of the Southeastern Conference on Combinatorics, Graph Theory, and ComputingUtilitas Mathematica Pub., 1974 - Combinatorial analysis |
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Page 96
... proof The proof will be given for the second formulation of the problem . It is based on the following variation of Dirichlet's " pigeon - hole " principle . If n boxes contain n objects and none of the boxes contains more than one ...
... proof The proof will be given for the second formulation of the problem . It is based on the following variation of Dirichlet's " pigeon - hole " principle . If n boxes contain n objects and none of the boxes contains more than one ...
Page 132
... Proof . The relations follow from the proof of theorem 4.2 . For the proof of the second statement , which uses the multiplicities of the eigenvalues , we refer to [ 6 ] or [ 8 ] . Certain regular two - graphs , in particular those ...
... Proof . The relations follow from the proof of theorem 4.2 . For the proof of the second statement , which uses the multiplicities of the eigenvalues , we refer to [ 6 ] or [ 8 ] . Certain regular two - graphs , in particular those ...
Page 558
... Proof : The theorem is trivial for k = 1 , 2 , or 3 as G is 5 - colorable , and it follows from theorem 1 for k = 4 or 5. The remainder of the proof is by induction on the number of vertices in G. We take ǝG to be the k - cycle V1V2 ...
... Proof : The theorem is trivial for k = 1 , 2 , or 3 as G is 5 - colorable , and it follows from theorem 1 for k = 4 or 5. The remainder of the proof is by induction on the number of vertices in G. We take ǝG to be the k - cycle V1V2 ...
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Common terms and phrases
1-factorization 5TH S-E CONF adjacency matrix algorithm automorphism balanced design blocks bound chromatic number circuit clique coloring COMBINATORICS complete components COMPUTING connected graph consider construction contains coordinate Corollary corresponding cosets cubic graph cycle defined degree denote digraph disjoint edges elements exactly example exists finite functions G₁ G₂ given graph G GRAPH THEORY Hamiltonian Hence homeomorphic independence graphs independent set induced intersection graph interval graph isomorphic Latin square Lemma Let G Math matroid maximum minimum forest n-coloring n-tuple nodes NP-complete number of vertices obtained optional points orbits pair palindrome parameters partition path permutation planar plane graph polynomial algorithm positive integers problem PROC Proof quadratic residue regular graphs result rows S₁ self-complementary self-dual codes sequence spanning tree starter strongly regular graphs subsets subsquare Suppose Theorem triple two-graph V₁ values vector vertex weight