## Fractional Graph Theory: A Rational Approach to the Theory of Graphs"This volume explores the various ways in which integer-valued graph theory concepts can be modified to derive nonintegral values. It explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics, including fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and additional subjects. 1997 edition"--Provided by publisher. |

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adjacency matrices algorithm assign bipartite graph chordal graphs clique compute conjecture contains Corollary covering number covering of H cycle double cover deﬁnition degree sequence denoted disjoint domination number doubly stochastic matrix dual duality edge chromatic edge chromatic number edge coloring edges of G elements exactly exercise ﬁnd ﬁnite ﬁrst fractional analogue fractional chromatic number fractional coloring fractional covering fractional matching fractional perfect matching fractional transversal fractionally Hamiltonian fractionally isomorphic function G and H graph G graph theory ground set Hamiltonian cycle hyperedges hypergraph independent sets induced subgraph inequality integer program kf(H Kneser graphs Lemma Let G linear program mad(G matching number Math MATHEMATICS matroid maximum number multigraph multiset Note number of G number of vertices optimal packing number permutation matrices planar graph polynomial poset positive integer Proposition Prove result satisﬁes subgraph of G subgraphs H subset sufﬁcient Suppose t-fold vertex vertex set vertices of G Xf(G