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AaAbAn adjacent algorithm alliance number assume baseline vertices basic blocks binary tree circ coloring communication sets complete bipartite graph complete graph computation congestion connected graph consider construct contain contradiction cutset cycle dd(G Definition deg(a deg(c deg(d deg(u deg(v deletion Department of Mathematics diam(G diameter distance double dominating set edge a-stable edge overlap elements equation Euler characteristic eulerian exactly exists a monochromatic family of graphs Figure free tetrahedron order free vertex graph G Graph Theory infinite family isomorphic labels leaf Lemma Let G m-near-A-fold Skolem sequence m-near-Skolem sequence Math median monochromatic solution multigraph network topology node number of links number of Ls number of straights number of subtrees odd number pairs polyominoes poset Proof rectangles rgood rooted binary tree routing table s-star sequence of order signed graph star stream cipher strings subgraph subgroup switches t-extended Theorem trominoes vertex a-stable vertices of degree