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Sum of squares of chromatic roots of a bipartite graph

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#combinatorics #graph-theory #coloring #algebraic-graph-theory #algebraic-combinatorics
82
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All DFT of binary numbers subsets of prime length are nonzero

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#elementary-number-theory #discrete-mathematics #fourier-analysis #algebraic-graph-theory
78
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Allocating one source to each islanded subgraph

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#discrete-mathematics #graph-theory #linear-programming #discrete-optimization #algebraic-graph-theory
42
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Adjacency matrix with Periodic boundary condition - Torus

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#linear-algebra #abstract-algebra #general-topology #graph-theory #algebraic-graph-theory
50
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Regular permutation groups and 2-closure

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#group-theory #graph-theory #permutations #automorphism-group #algebraic-graph-theory
268
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Number of $r$-colorings of a path graph with a specific color appearing $k$ times: A budgeted graph coloring

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#combinatorics #graph-theory #permutations #coloring #algebraic-graph-theory
65
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Why is the formula of edges$=$nodes$-$1 for modeling radiality very slow?

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#graph-theory #linear-programming #discrete-optimization #planar-graphs #algebraic-graph-theory
33
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Cycles of a graph may determine the characteristic polynomial of the adjacency matrix.

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#graph-theory #algebraic-graph-theory #characteristic-polynomial
59
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A poset $P$ is series-parallel iff it contains no subset isomorphic to $Z_4$

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#combinatorics #graph-theory #induction #order-theory #algebraic-graph-theory
60
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Why always the Crapo beta invariant value greater than or equal zero?

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#lattice-orders #combinatorial-geometry #algebraic-graph-theory #matroids #algebraic-combinatorics
80
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Proving that $ \beta(M) = \beta (M - e) + \beta (M /e).$

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#lattice-orders #combinatorial-proofs #algebraic-graph-theory #matroids #algebraic-combinatorics
34
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Let $A\subset B$ be flats of a matroid $M$ such that $r(A)=r(B)<\infty$. Then $A = B$.

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#combinatorics #algebraic-graph-theory #matroids #algebraic-combinatorics
62
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if $X$ is independent and $E(M) - X$ is coindependent, show that $X$ is a basis and $E(M) - X$ is a cobasis.

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#linear-algebra #independence #algebraic-graph-theory #matroids #algebraic-combinatorics
74
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Show that $C^*(e,B)$ is the unique cocircuit that is disjoint from $B - e.$

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#combinatorics #graph-theory #algebraic-graph-theory #algebraic-combinatorics #dualmatroids
72
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Understanding how to find the dual of a matroid.

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#combinatorics #graph-theory #algebraic-graph-theory #matroids #algebraic-combinatorics

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