def merge_vertex_covers(G, vertex_cover_1, vertex_cover_2):
    """
    Merge two vertex covers from edge partitions to get minimum vertex cover of G.
    
    Args:
        G: Graph represented as adjacency list/set of edges
        vertex_cover_1: Vertex cover for subgraph induced by E1
        vertex_cover_2: Vertex cover for subgraph induced by E2
    
    Returns:
        Merged vertex cover for the entire graph G
    """
    # All edges in the graph
    all_edges = G.edges()
    
    # Initialize merge process
    merged_cover = set()
    covered_edges = set()
    
    # Convert vertex covers to lists for merge-sort-like processing
    candidates_1 = sorted(list(vertex_cover_1), key=lambda x: G.degree(x), reverse=True)
    candidates_2 = sorted(list(vertex_cover_2), key=lambda x: G.degree(x), reverse=True)
    
    i, j = 0, 0
    
    # Merge process similar to merge sort
    while i < len(candidates_1) or j < len(candidates_2):
        # Calculate uncovered edges that each candidate can cover
        uncovered_edges = all_edges - covered_edges
        
        if not uncovered_edges:
            break
            
        # Get coverage count for remaining candidates
        coverage_1 = 0
        coverage_2 = 0
        
        if i < len(candidates_1):
            v1 = candidates_1[i]
            coverage_1 = count_edges_covered_by_vertex(v1, uncovered_edges)
        
        if j < len(candidates_2):
            v2 = candidates_2[j]
            coverage_2 = count_edges_covered_by_vertex(v2, uncovered_edges)
        
        # Choose vertex that covers more uncovered edges (merge-sort comparison)
        if i >= len(candidates_1):
            # Only candidates from cover_2 remain
            chosen_vertex = candidates_2[j]
            j += 1
        elif j >= len(candidates_2):
            # Only candidates from cover_1 remain
            chosen_vertex = candidates_1[i]
            i += 1
        elif coverage_1 >= coverage_2:
            # Vertex from cover_1 covers more (or equal) uncovered edges
            chosen_vertex = candidates_1[i]
            i += 1
            # Skip if same vertex exists in both covers
            if j < len(candidates_2) and candidates_2[j] == chosen_vertex:
                j += 1
        else:
            # Vertex from cover_2 covers more uncovered edges
            chosen_vertex = candidates_2[j]
            j += 1
            # Skip if same vertex exists in both covers
            if i < len(candidates_1) and candidates_1[i] == chosen_vertex:
                i += 1
        
        # Add chosen vertex to merged cover
        if chosen_vertex not in merged_cover:
            merged_cover.add(chosen_vertex)
            # Update covered edges
            newly_covered = get_edges_covered_by_vertex(chosen_vertex, uncovered_edges)
            covered_edges.update(newly_covered)
    
    return merged_cover


def count_edges_covered_by_vertex(vertex, edges):
    """Count how many edges from the given set are covered by the vertex."""
    count = 0
    for edge in edges:
        if vertex in edge:
            count += 1
    return count


def get_edges_covered_by_vertex(vertex, edges):
    """Get all edges from the given set that are covered by the vertex."""
    covered = set()
    for edge in edges:
        if vertex in edge:
            covered.add(edge)
    return covered


def find_vertex_cover_subgraph(edges):
    """
    Find a vertex cover for the subgraph induced by given edges.
    This is a simplified greedy approach for demonstration.
    """
    cover = set()
    uncovered_edges = set(edges)
    
    while uncovered_edges:
        # Find vertex that covers most uncovered edges
        vertex_count = {}
        for edge in uncovered_edges:
            for vertex in edge:
                vertex_count[vertex] = vertex_count.get(vertex, 0) + 1
        
        # Choose vertex with maximum coverage
        best_vertex = max(vertex_count.keys(), key=lambda v: vertex_count[v])
        cover.add(best_vertex)
        
        # Remove covered edges
        to_remove = set()
        for edge in uncovered_edges:
            if best_vertex in edge:
                to_remove.add(edge)
        uncovered_edges -= to_remove
    
    return cover