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Graph Coloring And Flows, Xiaofeng Wang
Graph Coloring And Flows, Xiaofeng Wang
Graduate Theses, Dissertations, and Problem Reports
Part 1. The Fulkerson Conjecture states that every cubic bridgeless graph has six perfect matchings such that every edge of the graph is contained in exactly two of these perfect matchings. In this paper, we verify the conjecture for some families of snarks (Goldberg snarks, flower snarks) by using a technical lemma.;Part 2. A star coloring of an undirected graph G is a proper vertex coloring of G such that any path of length 3 in G is not bi-colored. The star chromatic number of a family of graphs G , denoted by chis( G ), is the minimum number …
Hamiltonian Line Graphs And Claw -Free Graphs, Huiya Yan
Hamiltonian Line Graphs And Claw -Free Graphs, Huiya Yan
Graduate Theses, Dissertations, and Problem Reports
The research of my dissertation was motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Matthews and Sumner that every 4-connected claw-free graph is hamiltonian. Towards the hamiltonian line graph problem, we proved that every 3-connected claw-free Z8-free graph is hamiltonian, where Z8 is obtained by identifying one end-vertex of P9 with one vertex of a triangle; let hc( G) denote the least integer m such that the iterated line graph Lm(G) is Hamilton-connected, we showed that k -- 1 ≤ hc( G) ≤ max{lcub}diam(G), k -- 1{rcub}, where k is …
Numerical Solutions Of Boundary Inverse Problems For Some Elliptic Partial Differential Equations, Suxing Zeng
Numerical Solutions Of Boundary Inverse Problems For Some Elliptic Partial Differential Equations, Suxing Zeng
Graduate Theses, Dissertations, and Problem Reports
In this dissertation, we study boundary inverse problems for some elliptic partial differential equations. These are problems arising from quantitative analysis of various non-destructive testing techniques in applications. In such a problem, we are interested in using boundary measurements of the solution to recover either an unknown coefficient function in the boundary condition, or a portion of the boundary, or an unknown interior interface. We first introduce formulations of the boundary value problems into integral equations, then design numerical algorithms for solving each of these inverse problems. Numerical implementation and examples are presented to illustrate the feasibility and effectiveness of …