# Graph minor [electronic resource] /

Abstract (Summary)

Graph Minor Jianbing Niu In this paper, we present three results: (1) Let G be a (k + 2)-connected non-(k ? 3)-apex graph where k ? 2. If G contains three k-cliques, say L1, L2, L3, such that |Li ? Lj| ? k ? 2 (1 ? i < j ? 3), then G contains a Kk+2 as a minor. (2) Let G be a 6-connected claw-free graph. If ?(G) ? 7 and G contains three disjoint 5-cliques, say L1, L2, L3, then G contains a K7 as a minor. (3) There is a function h : N ?? N, such that, for every 4-connected graph G with minimum degree at least five embedded in a surface with Euler genus g and face-width at least h(g), every longest circuit of the graph G has a chord.
Bibliographical Information:

Advisor:

School:West Virginia University

School Location:USA - West Virginia

Source Type:Master's Thesis

Keywords:graph theory

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