weak immersionThe Kuratowski–Wagner Theorem asserts that a graph is planar if and only if it does not have either K3,3 or K5 as a minor. Using this, Wagner obtained a precise description of all graphs with no K3,3﹎inor and all graphs with no K5﹎inor. Similar results have been ...
MKK4 is a direct activator ofMAP kinasesin response to various environmental stresses or mitogenic stimuli. It activates MAPK8/JNK1, MAPK9/JNK2, and MAPK14/p38, but not MAPK1/ERK2 orMAPK3/ERK3. This kinase is phosphorylated, and thus activated by MAP3K1/MEKK (Wittenberger et al., ...
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Since K3,3 is 3-regular, the graphs with no K3,3-subdivisions coincide with the graphs with no K3,3-minors. These graphs will be referred to as K3,3-free graphs. By Wagner's theorem [20], a graph G is planar if and only if it does not have a minor isomorphic to K5 or K...
22 23 https://ubuntu.com/pro 24 25 Expanded Security Maintenance for Applications is not enabled. 26 27 0 updates can be applied immediately. 28 29 Enable ESM Apps to receive additional future security updates. 30 See https://ubuntu.com/esm or run: sudo pro status 31 32 Failed to ...
Projective㏄lanar Graphs with No K3, 4㎝inorAn exact structure is described to classify the projective-planar graphs that do not contain a K3, 4-minor. Copyright 2011 Wiley Periodicals, Inc. J Graph Theorydoi:10.1002/jgt.20603John Maharry...